Relaxation-cycle power generation systems control optimization Mariam Samir Ahmed

To cite this version:

Mariam Samir Ahmed. Relaxation-cycle power generation systems control optimization. Electric power. Université de Grenoble, 2014. English. ￿NNT : 2014GRENT019￿. ￿tel-01282457￿

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HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. THESE` pour obtenir le grade de DOCTEUR DE L’UNIVERSITE´ DE GRENOBLE Sp´ecialit´e: G´enie Electrique´ Arrˆet´eminist´eriel : 7 aoˆut 2006

Present´ ee´ par Mariam Samir AHMED

These` dirigee´ par Prof. Seddik BACHA et coencadree´ par Dr. Ahmad HABLY prepar´ ee´ au sein du Grenoble G´enie Electrique´ Laboratoire (G2ELAB) En collaboration avec Grenoble Images Parole Signal Automatique Laboratory (GIPSA-Lab) dans l’Ecole´ Doctorale:Electronique, Electrotechnique, Automatique, T´el´ecommunication et Signal

Optimisation de Contrˆole Commande des Syst`emes de G´en´eration d’Electricit´e`aCycle´ de Relaxation

These` soutenue publiquement le 28 F´evrier 2014, devant le jury compose´ de: M. Brayima DAKYO Professeur `al’Universit´edu Havre, France, Pr´esident M. Mohamed BENBOUZID Professeur `al’Universit´ede Brest, Rapporteur M. Rachid OUTBIB Professeur `al’Universit´ed’Aix-Marseille, France, Rapporteur M. Lorenzo FAGIANO Scientist at ABB Corporate Research, Switzerland, Examinateur M. Garrett SMITH Pr´esident et COO de Cosmica Spacelines, Examinateur M. Seddik BACHA Professeur `al’Universit´eJoseph Fourier, Directeur de th`ese M. Ahmad HABLY Maˆıtre de Conf´erences `aGrenoble INP, Co-encadrent de th`ese

D´edi´e`ala Syrie

Acknowledgment

Three years of my life went by, three years that shaped a new future for me, a future I didn’t know is been waiting for me. More than a scientific research trip, these years were a journey full of emotions, happiness, stress, homesickness and love. The journey wouldn’t have end successfully without the support, directly or indirectly, of many people that I would like to thank here.

Firstly, I would like to thank the thesis jury members I was honored to have to help con- clude this work: Mr.Dakyo the president of the jury, and Mr.Benbouzid and Mr.Outbib for their feedback and proofreading of the manuscript. Also I would like to thank Mr.Fagiano for making part of the jury and offering his expertise in a the novel field of kite-based systems, as well as Mr.Smith for the passionate discussions on renewable energy we had.

Back to 2010, For my master internship I was honored to work under the guidance of Professor Seddik BACHA, Professor Daniel Roye and Mathieu Hauk a PhD student at the time in the Electrical Engineering Laboratory G2ELAB. They introduced me to a very innovative interesting subject! Using Kites to generate electricity! I was completely concurred and when a PhD was proposed to continue on the same idea I jumped at the opportunity. I’m very grateful to having worked with M.Bacha et M.Ahmad Hably during my PhD, who I thank for their guidance and patience.

My gratitude goes to the staff of G2ELAB and GIPSA-Lab for the scientific friendly environment they offer, in addition to their help and guidance in the administration work.

Further, I would like to thank M.G´erard Meunier for welcoming me and helping me join the Master 2R - G´enie Electrique in INP, as well as my master friends who helped me catch up with them (being 2 months late for the course), we spent a great time preparing for exams, eating and partying together: Ionela, Minh, Christina, Julian, Luiz, Lyubo, Soul, Loic, thanh, and Hai, thank you so much. I won’t talk about this period without having a thought for my friend Moustafa to whom I own my deepest gratitude, he helped me settle down in Grenoble and taught me about adminstration work, university system among other things. Thank you Moustafa for everything.

Thanks for the thesis, I had the chance to be part of the OPLAT association with which 6 Acknowledgment

I spent a great year organizing activities in the lab, as well as the ZIK music group that was a relaxing escape during the hardest times. The thesis brought me also a great group of friends that I’m counting on keeping them forever: Nathalie, Raha, Angelina, Soulafa, Rachelle, Sinan, Antony, Bibi, and many other.

The best that the thesis has done was allowing me to meet my colombian soul mate Jos´e, something I wasn’t expecting at all when I first arrived to France. He was always there for me during both the happy and the sad moments. I would never be where I am now without you by my side. Thank you Josito for introducing me to your lovely family that I’m so proud to call mine.

My heart goes to my parents in Aleppo. My father who walked me, a little girl of five years old, and pointed stars to me and explain how the universe works in simple inspiring words. He would hand me over scientific books and teach me about electricity and statistics when I was eight. He implanted the passion for science in my heart and always encouraged me to follow this passion. Thank you mom for your encouragement and patience, I remember when I tried to help her with the house work she would always tell me to concentrate on my studies and that I ”will have the time to worry about these stuff later” even though she would have used some help being a working mom of four children, I wish to have half the energy you have when I become a mother. This work is dedicated to you dad and mom. Thank you my little brothers: Ahmad, Obada and Amr, for always supporting my decisions and enforcing my confidence by looking up to me and making me feel specially perfect for them. Contents

Acknowledgment 5

List of Acronyms xi

List of Notations xiii

General Introduction 1

I Relaxation Cycle Renewable Energy Systems 3 I.1 Introduction ...... 5 I.2 Renewable Energy ...... 6 I.2.a Global Energy Situation and Expectations ...... 7 I.2.b Renewable Energy Evolution ...... 9 I.3 Wind Energy ...... 10 I.3.a Conversion Technologies ...... 11 I.3.a-i Wind Turbines ...... 11 I.3.a-ii High Altitude Wind Energy Technologies ...... 13 I.3.a-iii Comparison between Different Technologies ...... 14 I.3.b Flexible Power Kites ...... 15 I.3.b-i Crosswind Kite Power ...... 16 I.3.b-ii Energy Generation ...... 18 I.3.c Kite-based System vs Classic Wind Turbine ...... 21 I.4 Wave Energy ...... 22 I.4.a Wave Average Power ...... 23 I.4.b Wave Energy Conversion Technologies ...... 24 I.4.b-i Near-shore WEC Systems ...... 24 I.4.b-ii Off-shore WEC Systems ...... 25 I.4.b-iii Comparison between Different Technologies ...... 26 I.4.c Vertically Oscillating Point Absorber Systems ...... 27 I.4.c-i Wave Energy Extraction ...... 27 I.4.c-ii Energy Generation Concept ...... 28 I.5 Relaxation Cycle Systems ...... 29 I.5.a Kite-based System’s Relaxation Cycle ...... 31 I.5.b Heaving Point-Absorber’s Relaxation Cycle ...... 32 I.6 Problem Statement and Objectives ...... 33 I.7 Conclusion ...... 33 ii CONTENTS

II Relaxation Cycle Systems: Structure and Modeling 35 II.1 Introduction ...... 37 II.2 Kite Generator System ...... 37 II.2.a KGS Structure ...... 38 II.2.a-i The Kite ...... 38 II.2.a-ii Kite Orientation ...... 40 II.2.a-iii The Tethers ...... 41 II.2.b KGS Modeling ...... 41 II.2.b-i Kite Dynamics ...... 43 II.2.b-ii Machine Applied Traction ...... 46 II.2.c Wind Speed Estimation ...... 47 II.3 Heaving Point-Absorber System ...... 47 II.3.a HPS Structure ...... 48 II.3.b HPS Modeling ...... 49 II.3.b-i Hydrodynamics Study ...... 49 II.3.c Power Maximization Techniques ...... 52 II.3.c-i Optimal Amplitude Control ...... 52 II.3.c-ii Optimal Phase Control ...... 53 II.3.c-iii Reactive Control ...... 53 II.3.c-iv Comparison ...... 53 II.4 Conclusion ...... 56

IIIKite Generator System: Supervision 59 III.1 Introduction ...... 61 III.2 Nonlinear Model Predictive Controller ...... 62 III.2.a Methodology ...... 63 III.2.a-i Primary Orbit Choice ...... 63 III.2.a-ii Orbit Optimization ...... 64 III.2.a-iii Orbit Period ...... 65 III.2.a-iv NMPC Design ...... 66 III.2.b Application ...... 67 III.3 Virtual Constraints-based Controller ...... 71 III.3.a Methodology ...... 75 III.3.a-i KGS Under-actuated Model ...... 75 III.3.a-ii Reduced Dynamics system ...... 76 III.3.a-iii Partial feedback linearization ...... 78 III.3.a-iv Controller Design ...... 79 III.3.b Application ...... 80 III.4Conclusion ...... 83

IV Kite Generator System: Grid Integration and Validation 85 IV.1 Introduction ...... 87 IV.2 Power Transformation System ...... 87 IV.2.a Torque Transmission between the Kite and the PMSM ...... 88 IV.2.b The PMSM’s Vector Model ...... 88 CONTENTS iii

IV.2.c Power Electronics Interface ...... 89 IV.3 Control Scheme ...... 90 IV.3.a Grid-connected operation ...... 91 IV.3.a-i Low Level Control ...... 91 IV.3.a-ii Intermediate Level Control ...... 92 IV.3.a-iii High Level Control ...... 93 IV.3.a-iv Maximum Power Cycle Tracking ...... 94 IV.3.b Stand-alone Operation ...... 95 IV.4 KGS Control Validation ...... 96 IV.4.a Real-time Hybrid Simulation Systems ...... 97 IV.4.b Power Hardware In the Loop Simulator ...... 97 IV.4.c KGS Implementation on the PHIL Simulator ...... 98 IV.4.c-i KGS Scaling ...... 98 IV.4.c-ii KGS Torque Emulation ...... 99 IV.4.c-iii Experimental Set-up ...... 101 IV.4.d Validation ...... 102 IV.5 Conclusion ...... 106

General Conclusions 109

VResum´ e´ Fran¸cais 111 V.1 Introduction ...... 111 V.2 Histoire ...... 112 V.2.a Energie Eolienne ...... 113 V.2.b Energie Eolienne A´eroport´ee ...... 114 V.3 Systeme` Gen´ eratrice´ de Cerf-volant ...... 116 V.3.a Structure ...... 117 V.3.b Mod´elisation ...... 118 V.4 Optimisation et Controleˆ ...... 119 V.4.a Commande Pr´edictive ...... 119 V.4.b Les Contraintes Virtuelles ...... 121 V.5 Integration´ au Reseaux´ ...... 126 V.5.a L’Interface de Transformation de Puissance ...... 126 V.5.b Validation ...... 128 V.6 Conclusion ...... 128

Bibliography 138

Publications 139

List of Figures

I.1 Norias on the Orontes river in Syria ...... 6 I.2 Important events in the history of energy...... 6

I.3 CO2 emissions evolution since 1965...... 8 I.4 Energy production history and expectations...... 8 I.5 Main renewable energy cumulative installed evolution between 1995 and 2012 (excluding hydro and bio-fuels)...... 9 I.6 Heron’s wind wheel used to supply an organ[Dra61]...... 10 I.7 A 1.5-MW wind turbine installed in a wind farm[TRV07]...... 11 I.8 Wind speed evolution with altitude above a flat open coast (γ = 0.4)...... 12 I.9 Off-shore wind turbine for the great lakes in Ontario-Canada [Flo10]...... 12 I.10 The balloon of Magenn Power Inc...... 13 I.11 Airborne wind turbines Imagined by Joby energy ...... 13 I.12 Imagined laddermill of Delft University of Technology ...... 14 I.13 Wright brothers Glider 1900...... 15 I.14 The Laddermill concept proposed by W.J. Ockels [MOS99]...... 16 I.15 Airborne wind energy research and development activities by country and by group as shown in the Airborne Wind Energy book [ADS13]...... 17 I.16 Refined crosswind law...... 17 I.17 An example of the pumping mode...... 19 I.18 An imagined Rotokite system used to pump water...... 19 I.19 Closed-orbit mode...... 20 I.20 Simplified presentation of the carousel of Kite-GEN ...... 20 I.21 Wave energy annual potential (kW/m)[Atl]...... 22 I.22 Regular wave parameters...... 23 I.23 Power per meter front for a regular wave...... 24 I.24 WAVEGEN simplified structure [BWF02]...... 25 I.25 TAPCHAN: Tapered Channel wave energy...... 25 I.26 PELAMIS wave energy system...... 25 I.27 Wave Dragon simplified structure [TPK09]...... 26 I.28 SEAREV basic principal [CBG05]...... 26 I.29 Imagined CETO submerged farm[Car]...... 27 I.30 A point-absorber system anchored to sea bed...... 28 I.31 A stable limit cycle ...... 30 I.32 The relaxation limit cycle solution of the Van-der-Pol equation with µ = 4...... 30 I.33 Example of power profile of a limit-cycle system...... 31 I.34 The pumping wing [LJADH12]...... 32 I.35 A simplified vertical displacement wave energy system...... 32 vi LIST OF FIGURES

II.1 Kite generator system structure...... 38 II.2 Kite’s main parameters and forces...... 39 II.3 Multiple-kite proposed structures [HD06]...... 40 II.4 The peter Lynn Bomba kite...... 40 II.5 The kite power region...... 41 II.6 Presentation of the kite’s multi-body model [WLRO08]...... 42 II.7 Lumped mass tether model [WLO07a]...... 43 II.8 Kite’s main forces...... 44 II.9 Kite’s attached coordinates...... 45 II.10 Definition of ψ and η angles...... 46 II.11 The HPS simplified structure...... 48 II.12 The upper bound of the possible absorbed energy from a sinusoidal wave...... 49 II.13 Cartesian coordinates linked to a floating body with 6 degrees of freedom...... 50 II.14 An irregular wave is the superposition of regular waves with random amplitudes and periods. 52

II.15 Floating body parameters, added mass mr and radiation parameter Rr...... 54 II.16 The resulted excitation force as a function of the wave parameters...... 54 II.17 Comparing generated Power in the case of a regular wave (H = 1.25m, T = 6.5sec). . . . 55 II.18 Jonswap spectrum of wave in Fig.II.14...... 55 II.19 Average power for regular (marked line) and irregular waves by applying reactive and optimal amplitude control...... 56 II.20 Absorbed energy without phase control (lower broken curve), with latching phase control (fully drawn curve) and with theoretically ideal optimum control (broken wavy curve). The curves show the wave energy (in joule) accumulated during 5 seconds...... 56

III.1 Illustration of model predictive control output...... 63 III.2 Initial orbit parameters...... 64 III.3 NMPC-based control strategy...... 67 III.4 Test orbits: Reference orbit (1) in continuous line, amplified orbits (2,3) in dotted line, and rotated orbits (4,5) in dashed line...... 68 III.5 Normalized and time dependent radial velocity in upper and lower figure respectively. Reference orbit (1): continuous, orbit (2): dotted, orbit (3): dashed...... 69 III.6 Normalized and time dependent radial velocity in upper and lower figure respectively. Reference orbit (1): continuous, orbit (4): dotted, orbit (5): dashed...... 70 III.7 KGS energy generation. Reference orbit (1): continuous. Upper plot: orbit (2) energy profile in dotted line, orbit (3): dashed. Lower plot: orbit (4) energy profile in dotted line, orbit (5): dashed...... 70 III.8 Starting from upper plot: The average mechanic power as a function of the kite surface

A, the inclination angle θ0; and the orbit rotation Rot...... 71 III.9 Tracking orbit 1 using optimal predictive control ...... 71 III.10Some motion and balance control problems solved using VC...... 72 III.11Example of a virtually constrained Two joint arm...... 73 III.12From the left: The indoors tethered-wing prototype of GIPSA-Lab and its representation. 75 III.13The reduced system periodic orbits...... 77 III.14Control block diagram...... 79 III.15The closed loop system’s portrait...... 81 LIST OF FIGURES vii

III.16The partial linear system closed loop evolution...... 81 III.17Evolution of state variables (θ, θ,˙ r, r˙) of the KGS...... 82 III.18The applied control for the studied KGS...... 82

IV.1 Kite Generator System Block diagram...... 88 IV.2 Modeling of the mechanic connection between the kite and the electrical machine. . . . . 88 IV.3 PMSM’s Behn-Eschenburg equivalent electrical model...... 89 IV.4 Electric representation of the PMSM-side converter. PMSM is presented by Behn-Eschenburg

model. Cdc is DC-bus filtering capacitor...... 90

IV.5 Electric representation of the Grid-side converter. Rf and Lf represent loss and filtering components...... 90 IV.6 General control scheme of the KGS power transformation system. Two control tracks applied depending whether the system is grid connected or in a stand-alone operation. . 91 IV.7 Low level control scheme for the machine-side converter...... 92 IV.8 Low level control scheme for the grid-side converter...... 93 IV.9 Intermediate level control scheme for the machine-side converter: Machine velocity control. 93 IV.10Intermediate level control scheme for the grid-side converter: DC-bus voltage control. . . 93 IV.11Optimal radial velocity as a function to time and wind speed...... 94 IV.12Inserting the MPCT algorithm in the NMPC-based proposed control strategy...... 95 IV.13Average output power of a 4-kite-based system...... 95 IV.14Load-connected converter low level control scheme...... 96 IV.15Machine-connected converter Intermediate level control scheme...... 96 IV.16PHIL Simulator ...... 98 IV.17Representation of the Mechanic connection in the case of the KGS and the DCM. . . . . 100 IV.18KGS replication using the DCM...... 100 IV.19KGS replication using the DCM...... 101 IV.20KGS real-time test platform scheme...... 101 IV.21KGS test bench control scheme...... 102 IV.22Optimal normalized radial velocity...... 103 IV.23Orbit Tracking using optimal predictive control. In green: Traction phase, in red: Recov- ery phase...... 104 IV.24Application of MPCT algorithm on the rotation velocity when wind speed changes from 4 to 5m/s at instant 40sec. Upper plot: In dashed red, the optimization resulted rotation velocity, in continuous blue, the MPPT rotation velocity. Center plot: The resistive

torque (CR), in dashed red, at wind speed 4m/sec, in continuous blue, at 5m/sec. Lower plot: The average mechanic power...... 104

IV.25Starting from the upper plot: The PMSM rotation velocity (ΩS ), PMSM phase current

(IaS ), DC bus voltage (UDC )...... 105

IV.26Starting from upper figure: Grid voltages, grid current (IaG), its frequency analysis. . . . 105

IV.27Starting from the upper plot: DCM torque (CDCM ), PMSM rotation velocity (Ωs), PMSM

phase current (Isa), and DC bus voltage (UDC )...... 106

IV.28Starting from the upper plot: PMSM rotation velocity (Ωs), grid phase current (Isa), and

grid phase voltage (VGa)...... 107 IV.29Zoom into the grid voltage and current changes when the PMSM changes its rotation direction...... 107 viii LIST OF FIGURES

V.1 The HPS simplified structure...... 112 V.2 Eolienne verticale `aNishtafun en Iran (600 AD)...... 113 V.3 Consommation mondiale d’´energie par type de ressource...... 113 V.4 Capacit´einstall´ee mondiale...... 114 V.5 Eolienne classique `atrois pales...... 115 V.6 Vitesse de vent en fonction de l’altitude...... 115 V.7 A gauche : Le prototype de Joby, `adroite : Le Makani M1 prototype...... 116 V.8 A gauche : Un cerf-volant de SkySails , `adroite : Un prototype de KiteGen...... 116 V.9 La g´en´eration d’´energie `abord (Mode de train´ee) vs la g´en´eration d’´energie au sol (Mode de portance)...... 117 V.10 Structure simplifi´ee de KGS...... 117 V.11 Les forces du cerf-volant...... 119 V.12 A gauche : l’angle de roulis, `adroite : l’angle d’attaque...... 119 V.13 Strat´egie de contrˆole utilisant la commande pr´edictive...... 120 V.14 Initial orbit parameters...... 120

V.15 En haut : La puissance m´ecanique moyenne en fonction de l’angle d’inclination θ0, en bas : En fonction de la rotation d’orbite Rot...... 121 V.16 Orbite param´etriques de teste...... 122 V.17 La vitesse radial optimale correspondante...... 122 V.18 KGS en mode pompage en deux dimensions...... 123 V.19 Diagramme de la m´ethodologie VCC...... 123 V.20 Le phase plot...... 125 V.21 D´eveloppement des variables du syst`eme...... 125 V.22 Evolution des variables du syst`eme...... 126 V.23 Repr´esentation ´electrique de la machine synchrone `aaimants permanents et les conver- tisseurs AC/DC et DC/AC...... 126 V.24 Chemin de contrˆole g´en´erale de l’interface de transformation de puissance...... 127 V.25 Repr´esentation du banc exp´erimental...... 128 V.26 Validation des chemins de contr ˆoles: A gauche en simulation, A droite sur le HIL simulateur.129 List of Tables

I.1 Energy consumption development by region: OECD and Non-OECD (Mil- lion tons oil equivalent) ...... 9 I.2 Enercon E33 main characteristics ...... 22

II.1 Test sea states ...... 56

III.1 Kite generator system parameters ...... 68 III.2 Testing orbits parameters and optimized orbits’ period, mean mechanical power and performance ...... 69 III.3 Coefficients for the simulation study...... 80

IV.1 Kite Generator System Parameters ...... 103

V.1 Les param`etres du syst`eme cerf-volant KGS ...... 121 V.2 La p´eriode et la puissance moyenne des orbites optimis´ees ...... 123

List of Acronyms

AWE Airborne Wind Energy DCM Direct Current Machine HPS Heaving Point-absorber System HAWE High Altitude Wind Energy KGS Kite Generator System NMPC Nonlinear model predictive Control OECD Organization for Economic Co-operation and Development PHIL Power Hardware In the Loop PA Point Absorber SM-PM Synchronous Machine with Permanent Magnets VCC Virtual Constraints-based Control WEC Wave Energy Conversion

List of Notations

Kite Generator System

A Kite’s area Ac Tether crosswind area CL Lift coefficient CD Drag coefficient Cdt Tether’s drag coefficient CR Kite’s resistive torque ~er Unit vector in the kite’s tether direction (~er,~eθ,~eφ) Kite spherical coordinates p ~ep Unit vector following W~ e ~eo Perpendicular on (~er,~ep) plan t Fgrav Tether’s weight t Faer Aerodynamic force F c,trc Tether’s traction force F~ grav Gravity force F~ app Apparent force F~ aer Aerodynamic force

F~L Lift force F~D Drag force F~ c,trc Tether traction force γ Surface friction coefficient g Gravity acceleration ~γ Kite acceleration Ge Kite aerodynamic efficiency coefficient J0 Normalized mean generated power p L W~ e amplitude µ Mass per length unit m Kite’s mass ΩS Rotor rotational velocity ψ Kite’s roll angle PM Mean generated power xiv List of Notations

R Rotor diameter r0 Initial tether’s length ρa Air density T Orbit’s period θ Tethers inclination angle v Normalized tether radial velocity V Wind speed VL Radial velocity V|| Crosswind speed W~ e Effective wind speed p W~ e Effective wind projection on (~eθ,~eφ) plan w|| Normalized crosswind velocity x Kite’s state vector ~xw Unit vector carried on the kite longitudinal axis ~yw Unit vector carried on the line connecting the kite’s tips ~zw Perpendicular on the kite surface and directed upwards z Altitude

Heaving Point-absorber System

ρ Water density H Wave amplitude T Wave period h Sea depth Si(w) Wave power spectrum λ Wave length d Point-absorber diameter Ew Wave energy V Point-absorber volume Pav Average power Pmax Maximum power CG Generator torque PA Optimum destructive interference power PB Budal upper limit power P Pressure on the floating point-absorber B Fluid’s external acceleration µ Fluid’s viscosity coefficient V Fluid velocity field φI Wave proper potential φD Diffraction scalar potential φR Radiation scalar potential ~n Unit normal vector on the floating body surface S Body’s surface ~r Unit rotational vectors List of Notations xv

m Floating body mass mr Added mass Rr Radiation damping coefficient z Point-absorber translation v Point-absorber translation velocity Fex Excitation force Z(t) Sea surface elevation Aˆn Normal distribution random wave amplitude Tn Normal distribution random wave period S Power spectrum RPTO Power take-off

Power Transformation Chain

CG Generator torque CDC DC-bus filtering capacitor D Damping factor estimation

esk : k = a, b, c Electromagnetic force voltage source in Behn-Eschenburg machine model φ¯fs Induced flow vector i¯s Stator currents’ vector i¯G Grid currents’ vector

IDCREC Machine converter output current IDC DC bus current J Total inertia of kite, drum; and machine’s rotor K Gearbox factor Kp Proportional gain Ki Integral gain Ls Inductance in Behn-Eschenburg machine model ω Machine’s electric pulsation ωG Electric grid pulsation ωn Resonant pulse of the injected currents harmonies p Poles’ pairs number Rs Resistance in Behn-Eschenburg machine model Rf ,Lf Loss and filtering components RDC DC-bus resistance Ti Corrector time constant UDC DC bus voltage v¯s Stator voltages’ vector VG Grid RMS voltage xvi List of Notations

Power Hardware-In-the-Loop

CDCM DC-Machine torque Ccor Correction torque JE Total inertia of the DCM and PMSM rotor DE Damping factor estimation between DCM and PMSM ΩE Rotor rotation velocity General Introduction

Answering for the growing demand for energy and the expectations of oil depletion, as well as, reducing the negative effects of human’s industrial and technological advance on earth’s climate are some of the most important issues facing us at present. One of the major challenges is how to decarbonize the electric grid by eliminating fuel-based electricity generators, and replacing them, preferably, by green and publicly accepted resources. That is where renewable energy resources rise as a promising solution. Lately, renewable energy has been undergoing a lot of research and development, that aims at solving renewable resources problems such as efficiency and grid integration, and exploring new methods and structures to exploit them. The later research axis led to the birth of relaxation-cycle renewable energy systems. Those have a periodic power cycle with two phases:

A generation phase during which the system is working in its “power” region, and • this enables it to generate electricity until it reaches its boundaries.

A recovery phase that resets the system’s state to start a new generation phase, and • consumes energy while doing so.

Hence, an optimization operation is required to insure the consumed energy’s minimiza- tion and the generated energy’s maximization. Relaxation-cycle renewable energy systems are the interest of this thesis. In particular, two examples of those are considered case studies. The first is the kite generator system (KGS). It is a solution proposed to extract energy from the steady and strong wind found in high altitudes. Its operation principle is to mechanically drive a ground-based elec- tric generator using one or several tethered kites. The second case study is the heaving point-absorber system (HPS), which is a floating wave energy system that employs wave oscillations to turn an electric generator and generate electricity. In addition to the classic problems accompanying renewable energy resources, those with relaxation-cycles are a very interesting field of open challenges, such as finding solutions to multi-dimensional optimization problems, and grid integration of their alternating out- put power. Those challenges are addressed in this thesis realized in Grenoble Electrical Engineering laboratory (G2ELab) with collaboration with Grenoble Image Parole Signal Automatique laboratory (GIPSA-Lab). The thesis is organized in four chapters: 2 General Introduction

The first chapter presents the Relaxation Cycle Renewable Energy Systems. It introduces the thesis subject and key words. It includes a brief overview on energy history, current situation and expectations, in addition to presenting the new technologies in the field of wind and wave energy while concentrating on those with relaxation cycles. The chapter also states the problems handled and the challenges confronted in the thesis, in addition to listing the objectives. The second chapter handles the Structure and Modeling of two relaxation-cycle systems. Those are the kite generator system and the heaving point-absorber system. Simplified structures of both systems are presented and modeled. Their relaxation cycle is defined and methods to maximize their generated power are listed. A comparison shows the re- semblance between both, and only the KGS is considered in the rest of the thesis. The third chapter deals with the Kite Generator System Supervision. Here, two strategies to optimize and to control the KGS are proposed. Those strategies are based on a nonlin- ear model predictive controller (NMPC) and virtual constraints-based controller (VCC). The last chapter is about the Kite Generator System Grid Integration and Control Val- idation. The topology applied to grid integrate the KGS or use it to supply an isolated load is modeled and controlled. Afterwards, the proposed control functioning is insured through simulations and experimental validation. It is achieved via testing on a power hardware-in-the-loop simulator which is real-time hybrid simulation system. Chapter I Relaxation Cycle Renewable Energy Systems

Contents I.1 Introduction ...... 5 I.2 Renewable Energy ...... 6 I.2.a Global Energy Situation and Expectations ...... 7 I.2.b Renewable Energy Evolution ...... 9 I.3 Wind Energy ...... 10 I.3.a Conversion Technologies ...... 11 I.3.b Flexible Power Kites ...... 15 I.3.c Kite-based System vs Classic Wind Turbine ...... 21 I.4 Wave Energy ...... 22 I.4.a Wave Average Power ...... 23 I.4.b Wave Energy Conversion Technologies ...... 24 I.4.c Vertically Oscillating Point Absorber Systems ...... 27 I.5 Relaxation Cycle Systems ...... 29 I.5.a Kite-based System’s Relaxation Cycle ...... 31 I.5.b Heaving Point-Absorber’s Relaxation Cycle ...... 32 I.6 Problem Statement and Objectives ...... 33 I.7 Conclusion ...... 33

Abstract

Triggered by the fear of oil depletion and dependence, an intensive research on alter- native to fossil fuels is going on recently. A huge part of this research is concerning renewable energy resources, and looks for new methods and technologies to improve their integration. An interesting and particular group of renewables assembles systems with relaxation cycles. Such systems need to regain periodically a state that allows energy production, which results in a recovery phase that consumes energy, hence a generation-consumption cycle is created and should be optimized to maximize the sys- tem’s average produced power. This first chapter presents the thesis main key words: Renewable energy, in partic- ular wind and wave energy, and relaxation cycle systems. It introduces, as well, the problems handled and the objectives of this PhD dissertation.

I.1. Introduction 5

I.1 Introduction

Modern civilization is very energy dependent, especially on its non-renewable resources that are expected to run out sooner or later, and shortly will not be able to satisfy the growing energy demand. The global demand in 2010, of which 86.5% is covered by fossil fuels [Pet10], is expected to increase by 40% in 2030. An increase that will not be ac- companied by a similar growth in fossil fuels production, and even if it does, new fossil fuels fields will be much harder to be dug out and exploited thus much more expensive. Thereby, demand increase must be covered by other energy sources. In addition, fossil fuels consumption should be limited as their usage is accompanied by emitting huge amounts of Carbon Dioxide CO2 which endangers the earth climate by its greenhouse effect [IEA11]. Renewable energy resources, such as solar, wind and tidal1 systems, rise as a very promis- ing ideal clean solution to cover for fossil fuels decline. Nonetheless, renewable energy generation is accompanied with a lot of scientific challenges, such as substitutability and intermittency [Fri10]. The major interest in sustainable development and the continuous research for new re- newable energy exploitation systems have led to the birth of a new family of systems: Those with relaxation-cycles. A relaxation-cycle system produces energy until it reaches certain limits after which it must recover a state that allows it to reproduce, this recovery operation could consume energy. Examples of those are: Kite-based traction and tidal systems that uses waves or swell energy. All renewable energy systems are more or less intermittent, but do not have major issues in terms of control. The problem is rather in improving their integration into the electric grid technically and economically. However, when considering power generation system with relaxation periodic phases, new difficulties are added. Firstly, providing the needed power during the recovery phase, and secondly, controlling the system’s generation/consumption cycle in order to recover the maximum possible energy. This should be achieved while considering the constraints on the system itself, the primary source of energy, and grid loads. In this first chapter, the thesis subject and objectives are introduced. It starts by an intro- duction on renewable energy history and expectations. Among the different investigated renewable resources, a couple is addressed in detail in Sections.I.3 and I.4: Wind Energy and Wave Energy. Classic and innovative methods to extract these energies are presented and compared, and examples of structures that employ the notion of relaxation cycles are as well introduced. Section.I.5 presents the relaxation-cycle system’s concept supported by some examples. Next, the problem’s statements and challenges, and the work objectives are addressed in Section.I.6.

1Tidal Systems should not be confused with the conventional hydraulic systems. 6 I. Relaxation Cycle Renewable Energy Systems

I.2 Renewable Energy

Renewable energy is the oldest exploited form of energy, starting from using wind energy to drive sail boats along the Nile more than 7500 years ago, and replacing man and animal effort by vertical wind mills in the middle east in 200BC, and by Norias2 (Fig.I.1) in Syria in 469AD [Bur63]. In Europe, windmills were the es- sential energy resource that supplied indus- try in the 12th century. Fig.I.2 displays a Figure I.1: Norias on the Orontes river in Syria time chart of some of the important events in the history of energy.

The development in renewable energy systems stopped and renewable resources 2E9&B:&I=A8&9A9D;K& %% &*+& became secondary in the 17th century, be- &&FB&8D=H9&E<=CE& cause of the arrival and the domination of !&%)'&$$! )*(!)&")"#'!) # &L&$ &*+& coal. Coal was the main reason for the in- 0=@C?9&I=A8&@=??E&=A&7<=A5&& " &*+& dustrial revolution in Europe around 1760. F&39DF=75?&5J=E&@=??E&=A&/9DE=5& It fed steam machineries and trains at the time, and later, in 1881, was used in first 4=A8@=??E&=A&,GDBC9& !!(%& electrical power generation plants3. The “Coal peak”, in 1873, created a fear +B5?&D9C?579&BF<9D& !' & of coal depletion, which regained renewable &:BD@E&B:&9A9D;K& energy attention back. The years 1883 to +B5?&/95>& !('#& 1891 witnessed many discoveries that con- -=DEF&I=A8@=??&FB& !(('& tributed to solar energy evolution, and in &;9A9D5F9&9?97FD=7=FK& 1891 the first solar cell appeared and the .=?&F&A5FGD5?&;5E&9@9D;98& !) & first solar heater was introduced. Further- 5E&9A9D;K&D9EBGD79E& more, in 1887 a windmill was used to pro- 1<9BDK&B:&B=?&C95>& !)%&& duce electricity for the first time. -=DEF&I=A8&FGD6=A9& !)' & Renewable energy resources were di- 0B?5D&:5D@E& !)( & minished again by the arrival of oil and /9FDB?&7D=E9E&& !)'#& natural gas at the beginning of the 20th century. Since then, fossil fuels are being heavily exploited in order to keep pace with /D9E9AF& the huge technological and industrial de- Figure-=DEF&85@& I.2: Important events in the history of en- velopment the twentieth century had wit- ergy. nessed. The problem is that fossil resources have

2Comes from the Arabic word Naaurah meaning the first water machine 3The very first electricity plant was a hydroelectric facility built on Niagara falls. I.2. Renewable Energy 7

been generated and stored underground since the birth of earth, billions of years ago, and are decreasing very fast that they will soon come to an end. This issue, in addition to some governments taking advantage of their fossil fuels and using it as a pressure to control international policy, has encouraged research to reconsider renewable energy as the future energy resource in fear of oil depletion and dependence. In the following, the current and future energy situation and the results of the current energy policy are discussed. As well as, some statistics on renewable and non-renewable energy evolution are presented.

I.2.a Global Energy Situation and Expectations

Many studies are carried on to predict future energy situation, and answer the questions:

How long oil will be able to satisfy its demand? • Will this demand continue to grow? • Those studies take into account many different variables [Fin08], such as proved reserve, expected population growth and economy evolution. They all agree on two points: First, the oil peak, or what is referred to as “Peak of the Oil Age”, if has not already occurred, it will very soon, some claims before 2020 [AHJ10]. Secondly, oil will become much more expensive, as it will be much deeper and more difficult to be extracted [HR11], and its production will not meet the demand level. In addition to limited future availability, fossil fuels are endangering the earth’s climate, because of their CO2 emissions. The emissions have already changed the earth climate dramatically during the last ten years due to global warming effect [IEA11]. Fig.I.3 shows how CO2 emissions have increased in the last two decades [Pet10]. Moreover, they are expected to grow 26% in 2030, according to the BP 2013 report, if the current global energy strategy were still adapted. The use of fossil fuels is a serious problem, not only economically and climate wise; but on the humanitarian side as well, as its lack has and will enhance wars. These threats to our earth have led to research replacing fossil fuels dependent machinery to electricity dependent ones; an electricity that is produced in a nature-friendly procedure. One non-fossil energy resource once considered very promising for future energy, is nu- clear energy. This resource, however, is facing many accusations considering its safety and cleanness. These accusations are now more intense after the recent Fukushima Daiichi nuclear disaster on March 2011 [Str11], which raised serious doubts about the future of nuclear energy. All mentioned points led to considering renewable energy resources, such as biomass, geothermal, solar photo-voltaic, solar thermodynamic, wind and tidal systems, as they offer the safest and cleanest type of energy. Fig.I.4 shows the evolution of energy production distribution by energy resource according to the BP4 energy outlook released in 2011[Pet10]. Though fossil fuels are expected to

4The British Petroleum society 8 I. Relaxation Cycle Renewable Energy Systems

Figure I.3: CO2 emissions evolution since 1965. continue to supply the majority of energy demands in 2030, renewable resources (wind, biofuels, hydroelectricity,...) are expected to witness a huge relative increase in the coming decade. For instance, renewable energy share in global energy consumption is estimated to have risen from 11.78% in 2011 to 13.20% in 2012, which means an 11.74% rise, of which, renewables’, other than hydro and bio-fuels, rise is estimated to 16.56% and have contributed 12.7% of world energy growth according to the latest statistics published by the BP society. Moreover, extensive studies are ongoing on how to extract energy from natural renewable resources and transform and inject it in the electric grid in order to increase renewable energy partition in future energy.

18000 2012 16000

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0 1990 1995 2000 2005 2010 2015 2020 2025 2030

Oil Natural Gas Coal Nuclear Energy Hydroelectricity Biofuels Other Renewables

Figure I.4: Energy production history and expectations.

Another objective is to increase investments and awareness on this field of energy should be achieved, mainly in the Non-OECD (Organization for Economic Co-operation and De- velopment) countries, whose share of energy demand is the largest according to Table.I.1. I.2. Renewable Energy 9

This can be achieved through collaboration between OECD and non-OECD countries via sharing information and advancements in renewable energy extraction technologies.

Table I.1: Energy consumption development by region: OECD and Non-OECD (Million tons oil equivalent)

Year 1995 2000 2005 2010 2015 2020 2025 2030 Total Energy Demand 8578 9382 10801 12002 13360 14627 15635 16632 OECD 4992 5435 5667 5568 5571 5679 5729 5765 Non-OECD 3586 3947 5134 6434 7789 8948 9906 10867

It may be somehow late to provide the needed energy using only non-fossil energy re- sources, but it worth working on to minimize the disastrous results of fossil fuels draining off.

I.2.b Renewable Energy Evolution

When electricity was first being produced in the late 19th century [Mar13], a huge part was due to renewable energy resources, mainly hydroelectric facilities. Apart from hydro- electricity, renewable resources provided expensive electricity compared to fossil fuels based generators. For instance: In 1940 in the USA, one kW h of wind-based generated electricity cost 12 to 30 cents, while a fossil fuel-based generated electricity cost only 3 to 6 cents/kW h [KS46], this price even declined to below 3 cents/kW h in 1970. The big difference in prices led to ignore renewable energy resources for the sake of fossil fuels and very limited improvement was done in this field.

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0 1995 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Geothermal Photovoltaic (PV) Wind turbine

Figure I.5: Main renewable energy cumulative installed evolution between 1995 and 2012 (excluding hydro and bio-fuels).

The crisis of 1973, as well as realizing that fossil fuels might come to an end one day or 10 I. Relaxation Cycle Renewable Energy Systems

another, forced politicians to adapt new policies to limit fossil fuels dependence, which gained back attention to renewable resources and nuclear plants. Since then, huge effort, development and research in the field were achieved. Cost was reduced and renewable energy share in power consumption has grown 5 folds from 0.43% in 1990 to 4.7% in 2012. As shown in Fig.I.5, wind energy contributed to the most substantial increment. During the last decade, wind energy global capacity increased more than nine-fold, growing from 17.4 GW in 2000 to 158.6 GW in 2009 [AWE10]. That makes wind, not only the fastest growing renewable energy resource, but also the fastest growing electric power resource of all [AJ05]. In the following, wind energy is addressed, as well as wave energy. Though wave energy does not represent a significant resource at present, it is believed to hold an important part in the future energy as it offer a dense and a vastly available storage of energy, and can be exploited without scenery negative effects.

I.3 Wind Energy

Human efforts to harness wind energy date back to the ancient times. This energy was employed to sail ships, grind grains, and pump water thousands of years ago. The first time man thought about using wind for mechanical power is believed to be during the seventeenth century B.C when the Babylonian emperor Hammurabi planned to use wind power for an ambitious irrigation project. However, the earliest documented design of using wind’s mechanical power to feed a machine is the wind wheel of the Greek engineer Heron of Alexandria (Fig.I.6) in the first century AD.

Figure I.6: Heron’s wind wheel used to supply an organ[Dra61].

Wind is considered an ideal renewable energy resource, since it is infinitely sustainable and clean, which explains the global interest in exploiting its energy. In the following, wind power conversion technologies are briefly presented and compared. I.3. Wind Energy 11

I.3.a Conversion Technologies

In addition to classic wind turbines, other solutions are proposed to harness wind power, including floating turbines that aims at capturing the strong offshore wind and structures that works at high altitude where strong stable wind is available continually.

I.3.a-i Wind Turbines

Traditionally, wind energy is exploited using a wind turbine (See Fig.I.7). Wind turbines technologies has evolved an varied greatly during the last 3 decades, however, a conven- tional turbine is a two/three-blade rotor, that captures wind’s kinetic energy. This is done by a direct, or through a gearbox, coupling with an electric generator. The turbine is con- nected to the electric grid directly or via a power-electronics interface. The turbine power is controlled by commanding the pitch and yaw blades angles. Notice that the eventual power electronics interface is exploited for this reason as well. The whole conversion chain and the blades’ control unit are placed up next to the rotor hub, on the turbine’s tower.

Figure I.7: A 1.5-MW wind turbine installed in a wind farm[TRV07].

Wind energy is written in eq.I.1, where ρ is the air density, A is the considered cross- sectional wind area, and V is wind speed. 1 P = ρAV 3 (I.1) 2

Hence, following the development of wind turbine’s industry, a trend to increase the size of the turbine is particularly clear. One aim of this increase is to reach higher altitudes where winds are supposed to be stronger and more stable since the aerodynamic friction of the earth surface slows down low altitude wind speed. This can be shown via the dependency function of wind speed V on altitude z:

z γ V (z) = v0( ) (I.2) z0 where v0 is the measured wind speed at an altitude z0, and γ is a surface friction coefficient. 12 I. Relaxation Cycle Renewable Energy Systems

The other objective is to increase the blades size thus the turbine working area, thus A, with which the available wind power increases linearly (eq.I.1).

Figure I.8: Wind speed evolution with altitude above a flat open coast (γ = 0.4).

Nevertheless, turbine size is not expected to grow as dramatically in the future as it has in the past without significant technological advancement and change in the design [TRV07]. As well as, despite the improvements of wind turbines efficiency, according to Betz limit [Gam07], it can only extract a maximum 59% of the available energy in an air stream with the same area as its working area. Moreover, although modern turbines are designed to capture 80% of this maximum limit, in reality their efficiency is about 40 50%. Besides, − the turbine does not produce its rated power continuously, due to wind irregularity. To overcome these limitations, new axes of research have started. One solution is building “Floating turbines” that take advantage of strong and regular open-sea wind (See Fig.I.9). The down point of this solution is that it does not solve the problem of costly construction and maintenance. The other solution looks for new flying structures able to extract wind energy at high altitudes (HAWE) of about 400 2000m. −

Figure I.9: Off-shore wind turbine for the great lakes in Ontario-Canada [Flo10]. I.3. Wind Energy 13

I.3.a-ii High Altitude Wind Energy Technologies

Several designs are proposed to harness HAWE, such as Air Rotor Systems, Airborne wind turbines and tethered airfoils (kites). The principle of the air rotor systems developed by Magenn (MARS) Power Inc[Meg], shown in Fig.I.10, is as follows: a helium-filled balloon stationary at an altitude between 200m and 350m rotates around a horizontal axis [OS92] in response to wind because of the magnus effect, generating electrical energy via a generator connected to its horizontal axis. The energy produced is then transmitted to the ground by a conductive cable. Magenn Inc. tested a 2kW prototype in 2008, and in 2010 has started manufacturing and commercializing a 100KW balloon.

Figure I.10: The balloon of Magenn Power Inc.

The second solution adapted by Sky WindPower [Skya], Joby energy [JE], and Makani Power [mak] is to use airborne wind turbines to harness energy directly in high altitude winds and send it to the ground through conductive cables. Fig.I.11 shows the airborne wind turbines proposed by Joby energy. This solution has some technical complexities, high cost and heavy structures. Only Makani Inc., acquired by Google.org as part of GoogleX, has passed to the production phase. They have already started producing a 1MW airborne wind turbine named “Makani M1”.

Figure I.11: Airborne wind turbines Imagined by Joby energy 14 I. Relaxation Cycle Renewable Energy Systems

The third option is to use power kites as renewable energy generators such as the “Kite Wind Generator” of Politecnico di Torino, and the “Laddermill” of the Delft University of Technology shown in Fig.I.12. In this case, mechanical power is generated when the kites are pulled by wind, transformed then into an electrical one using an on-ground generator. This allows the flying part of the system to be much lighter and avoid using conducting cables. This technology is expected to produce huge amounts of power using a much simpler and safer structure.

Figure I.12: Imagined laddermill of Delft University of Technology

I.3.a-iii Comparison between Different Technologies

After introducing the different proposed solutions to capture wind energy, in the follow- ing, the advantages and disadvantages of each solution are discussed. They are classified in three categories: Conventional wind turbines, airborne wind turbines and kite-based systems. From the grid connection point of view, wind turbines are not able to produce their rated power continuously, due to wind irregularity at their working altitudes, a problem that is less significant in the case of HAWE systems which are supposed to be working at an altitude higher than 400m where the winds are more regular. Concerning the quality of generated power, it depends whether the system returns power to the energy source or not, meaning whether it has a recovery phase or not. In general, a classic turbine has only one phase of functioning that is generation, which means that while generating, the resulted power is continuous as long as the turbine is in the power region limited by its cut-in speed and cut-out-speed. This is the case of stationary air rotor systems also. Meanwhile, kite-based systems and airborne wind turbines have a recovery phase whose goal is to maximize the average generated power and the respect of the systems constraints, but reflects negatively on the generated power which becomes intermittent. This, however, may be balanced out by the high reversibility of these systems that allows using two or more system with a suitable choice of the kite’s orbits to filter the resulted generated power. Furthermore, HAWE systems offer mobility and can be invested hugely as it works at a high altitude where strong wind could be present with little or no wind at low altitudes. Besides, they offer a very high adaptivity, as their rated power, as well as, generation/consumption phases, can be modified by changing the orbit the kite is following e.g. size, rotation I.3. Wind Energy 15

and/or inclination, or changing the altitude. Notably, a kite-based system rated power can also be adjusted by changing the kite surface. These adjustments are important to optimize the system’s generated power for changing conditions and constraints on it, e.g. Wind speed and direction. Cost-wise, HAWE systems economize the manufacturing, transportation and construction cost compared to a wind turbine, e.g. they eliminate the turbine mast cost. Finally, a kite-based System backs down when it comes to the real-time control issue. That is due to the complexity of the system’s behavior, a matter that will not be a problem thanks to the rapid development in computer and information technology, allowing to have fast and reliable real-time data processing. We are interested in HAWE relaxation-cycle systems, and particularly in kite-based sys- tem due to the advantages that can be obtained using it. This is the focus of the next section.

I.3.b Flexible Power Kites

Kites were used in China approximately 2,800 years ago. Apart from being child-toys, their early uses involved measuring distances, testing the wind, lifting men, signaling, and communication for military operations. After spreading in Asia, kites were brought to Eu- rope by Marco Polo at the end of the 13th century [Gom]. In the 18th and 19th centuries, in addition to military operations, kites were used to tow buggies in races against horse carriages in the country side [Gri09], and researchers like Alexander Graham Bell and the Wright Brothers invested kites in their development of the airplane, such as the Wright’s Glider 1900 shown in Fig.I.13. At the beginning of the 20th century, interest in kites was diminished by the invention of airplane [Sch12]. Kites drew back attention in 1972 when Peter Powell introduced a steerable dual lines kite, and flying kites became a sport. Af- terwards, in 1979, M.Loyd wrote a paper [Loy80] on how to use an airplane connected by a tether to generate huge amounts of energy. Though his paper was completely ignored at the time, it is now considered a revolutionary idea that will compute hugely in the future of renewable energy.

Figure I.13: Wright brothers Glider 1900.

It is not until 1996, however, that the idea was proposed again when W.J. Ockels regis- tered his Laddermill patent [Ock96] proposing the usage of kites connected in a cycle to turn an electric machine and generate electricity. Fig.I.14 shows the proposed Laddermill 16 I. Relaxation Cycle Renewable Energy Systems

Figure I.14: The Laddermill concept proposed by W.J. Ockels [MOS99]. structure of Ockels’s patent. Since then, few groups around the world have been working on this concept including Ockels team in T.U.Delft, Netherlands. For example, an Italian project named “Kitegen” was launched in 2007 in the Politecnico di Torino. A prototype was built and tested, but the project has unfortunately slowed down recently due to lack of investment and the division into two companies: KiteGen and EnerKite. Other university groups are carrying out these research, like for instance: K.U.Leuven in Belgium [FHGD11], the university of Heidelberg in Germany [DBS05][HD07], the uni- versity of Oulu in Finland [AS13]; and the university of Grenoble in France [AHB11a] [AHB11b][LJADH12]. In the industry sector, using flexible kites for towing ships is already in the market by Skysails GmbH Company in Hamburg, Germany [Skyb]. In fact, installing kites on huge ships proved to reduce their fuel consumption up to 30%, and now the company is study- ing the possibility of installing floating kite-based system in the sea to extract energy from off-shore strong winds. Some other companies’ names in the field include: Makani Power Company in the USA [mak], Windlift [Win], SwissKitePower [Swi], and Worcester Polytechnic Institute (WPI) project #DJO-0408 [Bal08]. Fig.I.15 lists some of the main projects in kite power field. New fabrication technologies permitted providing strong and light tethered kites, as well as, the huge development in electronics, communication, and computer sciences allows a fast and robust real-time optimization and control.

I.3.b-i Crosswind Kite Power

In his paper [Loy80], Loyd analyzed three ways by which the kite can generate energy. Two are significantly more effective:

The The drag power that can be exploited by having air turbines on the kite. This • idea was employed in the Air Rotor system and the airborne wind turbines presented in section.I.3.a-ii.

The crosswind power. Loyd showed that by neglecting the kite’s weight and the • tether effect, and considering the kite motion to be directly in crosswind5; then the

5This means the tether is parallel to the wind. I.3. Wind Energy 17

Figure I.15: Airborne wind energy research and development activities by country and by group as shown in the Airborne Wind Energy book [ADS13].

kite’s speed is increased significantly above the wind speed, which leads to increasing the can-be-generated power.

It is, however, not possible to let the kite fly always in a crosswind direction. In [ARS09], the refined crosswind motion low is found and expressed in eq.I.3. In the case of a small kite and a constant tether length, the refined crosswind formula is:

p W~ e = W~ e (~er.W~ e).~er, p − (I.3) We = G V | | e || where W~ e is the effective wind speed, that is the difference between the wind velocity W~ ~ ~ and the kite’s velocity Vk,(~er.We).~er is its projection on the tether direction, V|| is the crosswind speed and Ge is the aerodynamic efficiency.

Figure I.16: Refined crosswind law.

An eight-shaped trajectory of the kite is highly adapted, since it maximizes the apparent 18 I. Relaxation Cycle Renewable Energy Systems

wind blowing against the kite, and ensures the non-tangling of its tethers. But it should be mentioned that, according to [HD06], a circular trajectory will provide a 0.9% to 1.3% higher traction force than that of an eight-shaped one, in addition to ignoring the wind direction that may affect the system’s safety and control complexity [AC09]. Still, tethers tangling and coiling remain a serious problem and render the eight-shaped trajectory preferable.

I.3.b-ii Energy Generation

The concept is to mechanically drive a ground-based electric generator using one or several tethered kites6. Energy is extracted from high altitudes by controlling the kite to fly with a high crosswind speed. This develops a large pulling force that turns the generator, thus generating electricity. However, due to limitation in the tether’s length and the power region, the tether must be reeled in to its initial position, consuming energy as doing so. The system optimization will aim at maximizing the generated power and minimizing the consumption. The kite-based system should offer the tethered kite the flexibility to change its flying direction following the wind direction. In general, kite-based systems are classified in three groups according to the energy gen- eration concept:

The Pumping System7

It is largely adapted by several research teams. The system has two operation phases:

Traction phase, in which the kite is pulled by the wind, unrolling the tether which • turns the ground-based machine

Recovery phase, that begins when the tether reaches its predefined maximum length • or height, and needs to be reeled in, an operation that consumes energy.

To minimize this consumption the KiteGen project has presented two methods [FMP10]:

Low power recovery maneuver: The kite is driven to the borders of the “power zone” • defined later in Sec.II.2.a-i, where the aerodynamic forces become much weaker, and it can be recovered with low energy expense. One down point of this maneuver is that it occupies a huge space, which is a problem when it comes to considering a kite-farm for example.

Wing glide maneuver: Here the kite is controlled to be parallel to the tether, thus • it loses its aerodynamic lift and can return fast with low energy losses. Nonetheless, this maneuver, subject the system to instability and difficulty to restart its cycle.

Other than sequent eight-shaped orbits with increasing altitude that are usually adapted in the traction phase (see Fig.I.17)[AS10b], [LO05], [PO07a], [HD10], [CFM10], other ideas are also investigated. In GIPSA-Lab of Grenoble university, France, researchers are

6The generated mechanical power can be used directly to pump water or to tow a ship 7Referred to as the yo-yo mode of KiteGEN [CFM10], or the open-loop orbit of Argatov [AS10a]. I.3. Wind Energy 19

Figure I.17: An example of the pumping mode. working on a pumping kite in which the kite’s tether has a constant flight angle and the kite is controlled by its attack angle and traction force [LJADH12]. Apart from this, another idea started in SEQUOIA Company is the Rotokite. The idea proposes having two opposed kites connected to a single tether [Ver]. They are controlled to rotate around the tether, generating a lift force that will pull out the tether, and when the maximum height is reached, they are warped to minimize the aerodynamic lift and then pulled down.

Figure I.18: An imagined Rotokite system used to pump water.

The Closed-Orbit System

In this system, the kite is kept on a single eight-shaped orbit. During one orbit, two regions can be distinguished: A high and a low crosswind region. In the high crosswind region, the kite pulls out the tether which forms the “traction phase”, and in the low cross- wind region, the tether is reeled in, and that is the “recovery phase”. This mode may not generate as much energy as the pumping mode [AS10a], but it is easier to be stabilized and controlled, as it needs only one controller compared to at least two controllers in the pumping mode, as well as it occupies a small space [LW06]. Moreover, 20 I. Relaxation Cycle Renewable Energy Systems

its production can be optimized by a careful choice of the orbit and adding the possibility to control the aerodynamic coefficients through control of the kite’s attack angle [AS10a].

Figure I.19: Closed-orbit mode.

The closed-loop approach is principally used to tow boats and minivans [Bra10].

The Carousel System

This system, proposed by M.Ippolito [Ipp08], suggests placing several tethered-kites with their control units on vehicles moving along a circular rail path. Fig.I.20 shows a simplified presentation for the system. Vehicles’ speed is kept constant using electric machines on their wheels, while the kites tether’s length might be fixed or have a rolling/unrolling motion [CFM10]. For the first case, when the kite is in its power zone, it pulls the vehicle which presents the traction phase, and when the kite is out of the power zone it is moved back into it by the vehicle and that is the recovery phase. According to [FMP11], this complex structure generates the same power that can be produced using a simple pumping kite. Although by applying a rolling/unrolling (pumping) motion of the kite to compensate the consumed energy during the recovery phase, a highly efficient system can be obtained, it is still economically and technically very challenging. This proposed system is able to extract

Figure I.20: Simplified presentation of the carousel of Kite-GEN I.3. Wind Energy 21

huge amounts of energy, but it does not satisfy that a kite-based system is supposed to be largely lighter and cheaper than a classic turbine.

I.3.c Kite-based System vs Classic Wind Turbine

An example to compare a kite-based system to a classic turbine from the generated power point of view, is given in [Fag09]: A 2MW wind turbine, the weight of the rotor and the tower is typically about 300 tons, while a pumping kite-based system of the same rated power is estimated to be obtained using a 500m2 airfoil and 1000m long tethers, with a total weight of about 2 tons only. Practically, we mention here two examples of early trials in the field. In T.U.Delft, a one-tether kite control is tested in simulation; the kite surface is 25m2 with a mass of 50kg and the tether average length is 1000m. An optimal control is used to command the roll angle, attack angle, and the tether length variations rate. It uses different random guesses because there is no guarantee that the obtained solution is a global one. The average power generated depends on the orbit period, for example, a 60 sec period orbit yields in 75 kW [WLO07b]. The KiteGEN team has chosen a two-tether kite for their prototype, with control of the tether length variations rate and the roll angle. For simulation, a kite of 10m2 and 4 kg of mass; and maximum 800m long tethers. A nonlinear predictive control, without a pre-computed trajectory, is applied. It maximizes the average generated power directly. Besides, a sampling time of 0.2 sec is obtained by applying a fast nonlinear model predic- tive control (NMPC), for the sake of real time control computations. With a wind-speed of about 7.7m/s at 300m altitude, the average generated power is 5 kW [Fag09]. Furthermore, the following comparison is proposed to compare the efficiency of a kite-based system adopted in the next chapters and named Kite Generator System (KGS) compared to a classic wind turbine. Discussion A small Enercon wind turbine (E33) has the main characteristics of Ta- ble.I.2. Its rated power of 330kW can be obtained using the closed-orbit KGS described in Sec.IV.4.d but with a kite surface A = 300m2 = 30m 10m. The flying part of such a × system, including: the kite and the orientation mechanism will have a mass of less than 1t compared to about 18.7t for the E33 turbine’s on-tower mass, eg: excluding the tower and the turbine foundation. This fact makes the KGS easier to be transferred and maintained. On the other hand, both wind system occupy theoretically the same ground area. But when it comes to aerial area, the KGS’s power per unit area for this example seems to be about 60 times less than that of the E33, the same system can be used to produce more power by simply changing the kite’s altitude. As well, working at high altitude ensures a constant high wind speed hence constant power generation. Using a closed-orbit KGS is not suitable to compare the potential of using kites to produce electrical power to that of classical wind turbines, as its energy efficiency is small compared to the pumping KGS or a closed-orbit configuration with a variable aerodynamic efficiency Ge. 22 I. Relaxation Cycle Renewable Energy Systems

Table I.2: Enercon E33 main characteristics

Rated Power 300 kW Hub height 50 m Rotor diameter 33.4 m Rated wind speed 11.7 m/s

I.4 Wave Energy

Oceans store a tremendous amount of energy and are close to many concentrated popu- lations. This energy is stored in many forms. Most importantly in the form of flow, like tidal and marine currents, and waves and swells8. Wave power is receiving a particular attention lately due to its great potential, since waves are more constant and predictable than other types of renewable energy, as well as, their stored energy is very dense compared to that of wind and solar [BVJH09]. According to World Energy Council, wave energy technically available for extraction can satisfy 10% of the world electricity demand. In metropolitan France, this proportion is a little less, it is estimated to 40T W h, that is 7.27% of the 550T W h consumed per year in France [LP08].

Figure I.21: Wave energy annual potential (kW/m)[Atl].

France is a pioneer in the wave energy field. Historically, in 1799, in Paris, Girard and his son filled the first known patent to use energy from ocean waves, and in 1910, Bochaux- Praceique built an oscillating water-colomn device to employ wave power to supply elec- tricity to his house at Royan, in France. Wind waves are caused by the wind blowing over the surface of the ocean. They range between small ripples with approximately 10Hz frequency, that disappear once the wind

8The only difference between waves and swells is the distance from the source that has generated them, either local wind for waves or non-local for swells . For this reason, the word wave is used here to describe both. I.4. Wave Energy 23

stops, and 3.3mHz swells which are gravity propagated from wind-generated waves. Wind waves are distinct from longer wavelength waves caused by storms, earthquakes, e.g. Tsunamis, and those result from the Sun and Moon gravity, e.g. Tides. Since sea water density at the surface is about 1020kg.m−3 and that of air is 1.27kg.m−3 , waves travel much slower than the wind that created them, and the energy they can provide is compacted about 800 times. In fact, a wave power available for exploitation, given per wave front length unit, reaches a few tens of kW/m. For instance, wave annual average power on the Atlantic coasts is between 15 and 80kW/m [Mul03] which explains the particular interest in wave energy in the western coast European countries. Nevertheless, taking into account the difficulties facing wave energy development, including for example waves irregularity and weather conditions, a wave energy exploitation system will be a complex sophisticated one [CMF02].

I.4.a Wave Average Power

Sea level oscillations, just as wind, are stochastic space-time random phenomena. A sea wave can be approximated by a sine wave with both stochastic variable amplitude and period. Fig.I.22 presents the parameters of such a wave. Based on this wave definition,

Figure I.22: Regular wave parameters. one can find the wave front average power per meter [Fal07] in the case of deep water9 (See Fig.I.23): ρg2 P = H2T (W/m) (I.4) dp 16π and in the case of shallow water:

1 3/2 2 1/2 Psh = ρg H h (W/m) (I.5) (36π) where g is gravity acceleration, ρpis water density, H and T are the wave amplitude and period respectively, and h denotes the sea depth. The previous wave definition considers a pure sinusoidal wave with no obstacles, while in fact, a wave is irregular and defined as a superposition of multiple waves with random

9Water depth exceeds a third of the wavelength. 24 I. Relaxation Cycle Renewable Energy Systems

Figure I.23: Power per meter front for a regular wave. amplitudes and periods, as explained later in section II.3.b-i. In [GHG10], sea behavior is defined as a group of sea states, where each state i has an average power given by:

∞ i i i Pirr = P (H, w)S (w)dw (W/m) (I.6) Z0 where Si(w) is the power spectrum of the wave at the state i for the frequency w, and P i(H, w) is the average power of a regular wave with (H, w) as parameters. The irregularity and the slowness of waves oscillations, make transforming their energy into an electrical form, that can be later commercialized, very challenging.

I.4.b Wave Energy Conversion Technologies

Several solutions are proposed to extract wave energy and convert it into electricity [Fal10] are proposed [AMCHB12][BEBC07]. Wave energy conversion (WEC) systems can be categorized based on the location and the depth they are designed to work at, i.e. Near- shore and off-shore systems.

I.4.b-i Near-shore WEC Systems

They are mainly turbine-based structures; their operating principal is to employ waves oscillations to generate a current of water or air that turns a turbine coupled with an electric machine, thus generating electricity. As examples of these systems one can cite:

WAVEGEN (4 MW)10 In this system, an air turbine is turned by the air current gen- • erated by waves oscillations (Fig.I.24). It has been already installed and connected to the Spanish electric grid in 2009.

TAPCHAN (Tapered Channel) Wave Energy (rated output about 350 kW) [Tju94]. • Shown in Fig.I.25: This construction canalizes sea water to turn a turbine, then water flows from the basin back to the ocean by gravity. It was first constructed in 1985 and installed in Norway.

10http://www.unenergy.org I.4. Wave Energy 25

Figure I.24: WAVEGEN simplified structure [BWF02].

Figure I.25: TAPCHAN: Tapered Channel wave energy.

I.4.b-ii Off-shore WEC Systems

Here, floating systems emerged among others as the most important logic solution to capture waves. They capture waves oscillations and transform them into translational or rotational movements, that generate electricity via an electrical machine. Floating WECs are classified in three categories:

Attenuators, or linear absorbers: It is a large linear structure directed to be • parallel to the wave propagation, and composed of jointed segments that rotates relative to each other harnessing the waves power as doing so. An example of at- tenuators is PELAMIS (up to 2.25 MW) [YHT00]. It is a series of semi-submerged cylindrical sections linked by hinged joints (Fig.I.26). The sections move relative to one another as waves pass. This motion is employed to generate electricity using hydraulic pumps. These systems are developed by a Scottish company (PELAMIS wave power), and was first connected to UK grid in 2004.

Figure I.26: PELAMIS wave energy system. 26 I. Relaxation Cycle Renewable Energy Systems

Terminators, It is a perpendicular-to-the-wave construction. An example of those • is the Wave Dragon (7 MW), which is an overtopping terminator whose objective is to guide waves to form a vertical water current employed to turn a turbine. A 20 kW prototype was already tested in 2003 in Denmark [TKKFM06]. This project is now in its final stages to deploy a full-scale system connected it to the electric grid. Fig.I.27 shows its simplified structure.

Figure I.27: Wave Dragon simplified structure [TPK09].

Point Absorbers (PA): Contrary to former types, point-absorbers are small struc- • tures. They capture wave energy in all directions, and might be fully or partially submerged. Examples of PAs include:

– SEAREV (Independent Electric Wave Energy Recovery System) (500 kW) [RBMJ10]: It is a project in France (Ecole centrale de Nantes). In this float- ing semi-submerged system a moving mass oscillates due to waves, and these oscillations are transformed into electrical power by means of hydraulic pumps or an electrical generator [AMBA09]. Fig.I.28 presents the basic principal of SEAREV.

Figure I.28: SEAREV basic principal [CBG05].

– CETO (5 MW)[Car] It is a pumping and desalination system. A small scale commercial demonstration project was constructed and tested in Garden Island in Western Australia. Fig.I.29 shows an imagined CETO farm.

I.4.b-iii Comparison between Different Technologies

Although near-shore WECs are easier to be installed and maintained, they are far from the powerful waves that lose most of their energy before reaching the coast, and they face public rejection as they damage the coastal rich underwater life and the scenery. I.4. Wave Energy 27

Figure I.29: Imagined CETO submerged farm[Car].

As will be explained later, in order to capture a maximum of the incident wave power, the floating body natural frequencies should contain that of the wave. Terminators and attenuators have a wide bandwidth which give them greater chance to harness most of the wave power, while the point-absorber which is a relatively small structure has a narrow bandwidth which applies that it should be controlled to enlarge it to contain the wave frequency. However, according to [BF75], smaller volume of the point-absorber increases P the ratio potentially converted power to volume V . One advantage of attenuators is their sensitivity to small amplitude wave oscillations. As terminators employ turbines to harness wave energy, just like classic hydroelectric devices, they are easier to be modeled and controlled as the turbine-based technology is already well studied and researched. Still the means by which the terminator canalize water to traverse the turbine, makes the hydrodynamics very non-linear and not possible to be solved by the linear wave theory [Fal10]. Point-absorber systems are mostly designed so that their power transformation parts, mechanical, hydraulic or electrical, are enveloped and isolated from seawater, which yields longer lifespan and less maintenance.

I.4.c Vertically Oscillating Point Absorber Systems

A vertically oscillating point absorber system harness energy from the up and down waves motion. The device dimensions are small compared to the wave length. It is typically used to absorb energy from waves of 40 to 300m length. It can be partially or totally submerged. Fig.I.30 shows a point-absorber system anchored to sea bed. An example of these systems is the Ocean Power Technology’s Power-buoy. It is a floating buoy that has two rods attached to piston within a cylinder. As the vertical movement of the buoy causes these pistons to rise and fall as well, pumping ocean water through a turbine that generates electricity.

I.4.c-i Wave Energy Extraction

In order to capture the wave energy, basic energy conservation law apply that the point absorber should reduce the wave power. Hence, it should generate an opposing wave that interferes destructively with the original wave, which implies that in order to be a good point absorber, an object should be a good wave generator [Fal07]. 28 I. Relaxation Cycle Renewable Energy Systems

Figure I.30: A point-absorber system anchored to sea bed.

Nevertheless, there is always a maximum possible extracted power from the wave, because of the point absorber geometry. For example, in the case of a regular wave whose power Ew, a ring-shaped wave generator point absorber can absorb a maximum power of:

λ ρ(g/π)3 P = E = H2T 3 (I.7) max 2π w 128 where λ is the wavelength.

I.4.c-ii Energy Generation Concept

A point-absorber energy generation concept depends whether its vertical displacement is controlled or not, and if it is, what the applied control method is. According to this we classify point-absorber systems in three categories11.

Passive Point-Absorber

In the case of applying no control on the point-absorber, it exhibit slow oscillations fol- lowing the wave and capture a part of its energy by means of its resistive inertia. The resulting performance is poor and depends on the geometry of the point-absorber. In order for the point-absorber to generate an optimal destructive wave, its oscillations amplitude and phase should be optimized. A control is important to protect the system by respecting the functioning limits, such as the oscillations maximum amplitude.

Latched Point-Absorber

The point-absorber wave must be in phase with the original wave. This can be obtained by using a sufficiently large oscillating point-absorber whose bandwidth is wide enough to contain an approximate optimum phase for all frequencies within the wave spectrum, and, in the case of a reasonable-sized object, applying a control method to shift the bandwidth to contain the optimal phase. This can be achieved by blocking the floating body for a suitable time interval, then let it

11Only the most common used techniques are chosen. I.5. Relaxation Cycle Systems 29

go when it arrives to the optimal phase position.

Reactive Point-Absorber

In a reactive point-absorber, both the phase and the amplitude of the oscillation are optimized, this requires returning some energy to the system.

I.5 Relaxation Cycle Systems

After addressing renewable energy history, importance and technologies to exploit it, this section is dedicated to a particular type of renewable energy systems, those of relaxation cycles. Some keywords that lead to the the definition of relaxation cycle systems are pre- sented. Those are:

Nonlinear Systems

A nonlinear system is a system that does not satisfy the superposition property of lin- ear ones: f(αx + βy) = αf(x) + βf(y) (I.8) Which means that the effect of inputs is not additive neither changes in proportion to changes in the inputs. These systems are particularly important to physicians and engi- neers since most, if not all, physical systems are naturally nonlinear. A dynamic nonlinear system is expressed by nonlinear differential equations that relate its outputs to its inputs. An example of nonlinear differential equations are the Navier-Stokes equations in fluid dynamics. The main significant difference between nonlinear and linear equations is that two solutions can not generally be combined to form a new one which is a result of the superposition property of eq.I.8. A dynamic nonlinear system exhibits periodic oscillations when its differential equations have a nontrivial T-periodic solution:

x(t) = x(t + T ) t > 0 (I.9) ∀

Limit Cycles

In the dynamic systems area of interest, a limit cycle is, as first introduced by Henri Poincar´ein 1882 [KI98], an isolated closed trajectory in the phase space; in other words, its neighboring trajectories spiral either towards or away from it. In this context, limit cycles can only occur in nonlinear systems, since in a linear system exhibiting oscillations closed trajectories are neighbored by other closed trajectories. That leads to the definition of a stable limit cycle, whose neighboring trajectories always spiral to it when time goes to infinity. Fig.I.32 illustrates this definition. A system with a stable limit cycle can exhibit self-sustained oscillations, and the system goes always back to the limit cycle in the case of disturbance. Oscillations of this type are 30 I. Relaxation Cycle Renewable Energy Systems

called relaxation oscillations.

Figure I.31: A stable limit cycle

Relaxation Oscillations

They are nonlinear oscillations obtained by increasing a constraint continuously, then loosening it suddenly. When the constraint becomes very strong, the resistant part gives in abruptly and a part of the energy is evacuated. The constraint then re-increases and the cycle restarts. To demonstrate, we consider few examples. A classical one is the Pythagorean cup expe- rience, where the constraint is the water level which increases continuously thanks to the arriving water,then it drops sharply when the trap is triggered. A second example is the Van-der-Pol oscillator expressed by eq.I.10.

x¨ + µx˙(x2 1) + x = 0 (I.10) − with µ >> 1.

Figure I.32: The relaxation limit cycle solution of the Van-der-Pol equation with µ = 4.

Many examples of such oscillations can be obtained by applying certain electronic config- uration, as for instance, charging slowly a capacitor until it reaches a predefined value, then discharge it rapidly using a controlled switch. I.5. Relaxation Cycle Systems 31

Power Relaxation Cycle

Power relaxation cycle systems particularly concern power generation systems character- ized by a cycle composed of two phases: a phase of slow recuperation of power followed by a fast phase of power release. The power release phase is needed to re-initiate the system state in order to start a production phase. Both phases are optimized and controlled to so that the cycle overall power is positive. The power profile of a power relaxation cycle system can take the form shown in Fig.I.33.

Figure I.33: Example of power profile of a limit-cycle system.

Examples of such systems include Kite-based traction systems, some wave power systems and renewable-based thermic systems. These systems pose a new scientific problem that is to control the generation/consumption limit cycle in order to maximize the generated power while respecting the various constraints on the system itself, the primary energy source, and the grid or the loads. Next, two examples of power relaxation cycle:

I.5.a Kite-based System’s Relaxation Cycle

Depending on the kite-based system power generation concept and structure, the system can be a power generator all the time or a limit-cycle system that periodically gener- ates/consumes power. An example of the former is the carousel configuration with variable tether length (see Sec.I.3.b-ii), and the dancing kites [KAB08] that involves connecting two kites to the same generator, and control them contrarily, in order to have a positive energy all the time (Fig.II.3-b). Theoretically, when properly controlled, this type of systems does not present new chal- lenges compared to classic renewable energy source (RES). Nevertheless, a simpler kite- based system has a periodic generation/consumption power profile. This system uses a kite or an airborne wing to harness wind energy at high altitudes and transform its kinetic power into mechanical one by means of a tether coupled to a ground- based machine. The kite cannot pull infinitely as the tether length is limited, and should be periodically redrawn down to restart the pulling phase. Therefore, the kite or the wing control is designed to establish a relaxation cycle at the end of which, the system’s flying part restores its initial position. The relaxation cycle is chosen to be in the kite’s power region, to respect the system’s 32 I. Relaxation Cycle Renewable Energy Systems

Figure I.34: The pumping wing [LJADH12]. physical limits (e.g. the maximum flight angle, the tether maximum traction and length; and the machine’s maximum rotation velocity), and to maximize the average generated power. The pumping wing of [LJADH12] serves as a simple example of such a performance. It is shown in Fig.I.34. The wing moves up and down while keeping a fixed inclination angle with the ground. While moving upwards the wing’s attack angle is kept at a great value in order to produce a high lift force, and when moving downwards the angle of attack is reduced to a minimum value, so that the wing is almost parallel to the tether, and a small traction is needed to recover the wing’s initial position.

I.5.b Heaving Point-Absorber’s Relaxation Cycle

Another example of a relaxation-cycle renewable energy system is the vertical displacement wave energy one shown in Fig.I.35. It is composed of a floating part that has a single degree of freedom that is vertical displacement following z. This displacement is transformed into rotational movement using pulleys. The system displacement is controlled to maximize

Figure I.35: A simplified vertical displacement wave energy system. the harnessed wave energy by having a pattern chosen depending on the observed waves characteristics. That means, at some point the system consume a portion of energy to insure the optimal pattern. To clarify this point, let’s consider the optimal phase control I.6. Problem Statement and Objectives 33

proposed in [BDC04], [FJH09] and [Fal02]. It can be achieved by applying a latching control that blocks the floating body for a suitable time interval, then let it go when it arrives to the optimal phase position. Applying this latching create a relaxation cycle in the system.

I.6 Problem Statement and Objectives

Renewable energy systems with relaxation phases differ from those conventional systems in adding new challenges when considering their control and integration on the grid. The system’s cycle should be suitably chosen in order to maximize the average generated power, while keeping the system within its physical limits. This is a spacial-temporal optimization problem that needs to be solved. Another criterion to optimize is to maximize the system performance; e.g. The ratio between the average power Pav and the maximum power Pmax: P µ = av (I.11) Pmax This avoids using over-sized system’s components, as for instance electric machines, in order to obtain only a small portion of the power they are designed to pass. In addition to the optimization problem, the systems dealt with are usually complex non- linear ones that require high level of modeling and advanced control techniques to stabilize and control them. Another aspect to handle is the integration of relaxation-cycle systems on the electric grid. Those systems require a bidirectional interface with the electric grid, as well as, a storage unit in the case of a connection to a load or an isolated grid, which adds to the complexity of control and power management in the system. This may seem similar to wind turbine’s with a storage to balance wind turbulence and an emergency stop mechanism, however, in the case of a relaxation cycle system, the system changes its status between generator and load periodically and relatively fast which requires the problem to be dealt with differently. The above mentioned problems are discussed and solutions are proposed and tested through- out the rest of this thesis. Two systems are considered as case-studies: The kite generator system proposed in Section.I.5.a and the heaving point-absorber system of Section.I.5.b.

I.7 Conclusion

In brief, this chapter provided a mapping of current technologies proposed to exploit wind and wave energy, with a special attention to those employing relaxation-cycle systems. A booming question is being asked a lot at present: What is today’s energies’ future? Fossil fuels are not expected to answer the growing energy demand for a long time, and they are getting more and more expensive due to the technical difficulties accompanying exploiting newly explored fields. These reasons claim searching new solutions for energy production. Among proposed solutions, renewable energies offer a clean, safe and sustain- able substitute to fossil fuels. 34 I. Relaxation Cycle Renewable Energy Systems

Here, renewable energy systems with relaxation cycles are considered. They are a newly explored class that emerged from the recent research in the field of high altitude wind energy, wave energy and thermal energy. They are characterized by a power cycle that has two phases: A generation and a recovery phase, and the difficulties arise when it comes to optimizing and controlling this cycle in order to maximize the generated average power, and when the system is used in an isolated grid. Chapter II Relaxation Cycle Systems: Structure and Modeling

Contents II.1 Introduction ...... 37 II.2 Kite Generator System ...... 37 II.2.a KGS Structure ...... 38 II.2.b KGS Modeling ...... 41 II.2.c Wind Speed Estimation ...... 47 II.3 Heaving Point-Absorber System ...... 47 II.3.a HPS Structure ...... 48 II.3.b HPS Modeling ...... 49 II.3.c Power Maximization Techniques ...... 52 II.4 Conclusion ...... 56

Abstract

In the scope of relaxation-cycle systems and their contribution for electricity gener- ation, the two examples presented in Chapter I are studied and modeled here. The kite-based wind system, named thereafter the kite generator system (KGS), and the floating point-absorber wave system named heaving point-absorber system (HPS) rep- resent two emerged important classes of renewable energy systems whose early tests have shown promising open problems.

II.1. Introduction 37

II.1 Introduction

The optimization and the control of relaxation cycles renewable energy resources require, as a first step, finding a model for the system in order to achieve better understanding of its behavior. While the kite generator system (KGS) is chosen to be studied thoroughly in this thesis, an example of point-absorber wave systems, that is a heaving point-absorber system (HPS), is studied and modeled as well in order to show its similarity with the KGS and how it may be controlled in the same manner in order to maximize its cycle average generated power. In this chapter, the structure of the proposed systems, as well as the model of each are developed. KGS found models will be used to design the control strategy and will be implemented on Matlab/Simulink in order to test this strategy (section III.3.a-iv). They are also used to emulate the system’s behavior by a physical component, a torque controlled DC-machine, on the real-time experimental platform presented in Chapter.IV.5. The chapter is divided into two main sections. The first part is devoted to the KGS. It starts with presenting the chosen structure and its main components. Next, it introduces the dynamics of the kite and how its traction is transferred to the ground to serve as a torque applied on an electric machine. The second part handles the HPS. It presents and models the system, and go over the techniques to maximize its average generated power.

II.2 Kite Generator System

As shown in Fig.II.1, a simplified kite-based system is composed of a kite connected to a drum by a tether. The drum changes the traction force generated by the kite into a resistant torque applied on an electric machine through a gearbox. The machine converts this mechanical traction to an electrical energy that can be later stored or injected in the electric grid. In a closed-orbit scenario, energy is extracted from high altitudes by letting the kite fly on a closed lying-eight orbit with high crosswind speed [FMP09]. While tracking the orbit, two phases are distinguished: A traction phase, through which the KGS develops a large traction force that turns the electric machine, thus generating electricity, and a recovery phase, through which the kite is pulled by the machine, consuming energy as doing so. The objective is to improve the traction/recovery cycle through controlling the kite’s position and movement around a predefined optimal trajectory that depends on wind’s direction and speed. This mode’s efficiency is 16 times less than that of a pumping system presented in Sec.I.3.b- ii [AS10a]. But it can be improved 5 times by varying the aerodynamic efficiency [AS10a]. The closed orbit system is easier to be stabilized and controlled, as it only needs one controller, it also occupies a smaller space compared to an opened loop or a carousel configuration (sec.I.3.b-ii)[LW06]. 38 II. Relaxation Cycle Systems: Structure and Modeling

Kite

Eight-shaped Orbit

Orientation mechanism

Tether

Power Transformation Drum

Figure II.1: Kite generator system structure.

II.2.a KGS Structure

Different research teams have adopted slightly modified structures from the basic one in Fig.II.1. They vary in the number of kites and tethers, the implemented orientation mechanism, as well as the used materials. In the next paragraphs, each part of the KGS is presented in more details and different designs are overviewed.

II.2.a-i The Kite

In the KGS, the kite represents the effective wind power harnessing part of the system.

Kite’s Parameters

Just like an airplane wing, a kite is characterized by two main parameters: its aspect ratio AR and its aerodynamic efficiency Ge. The aspect ratio is the ratio between the kite span ws and chord c (see Fig.II.2-(a)), meanwhile, the kite efficiency is the ratio between its lift coefficient CL and drag coefficient CD. These coefficients are functions of the kite’s attack angle α, that is the kite angle with the effective wind We (The difference between the wind speed and the kite’s velocity.)

Kite’s Forces

The forces acting on the kite can be summed up in (see Fig.II.2-(b)):

F~ = m~g the gravity force, where m is the kite mass and ~g is the gravity acceler- • grav ation.

F~ the apparent force which results from the kite’s acceleration. • app II.2. Kite Generator System 39

Figure II.2: Kite’s main parameters and forces.

F~ aer the aerodynamic force which can be decomposed into: A lift force F~ that is • L perpendicular to the kite’s surface A, and a drag force F~D which has the effective wind’s direction W~ e. Eq.II.1 presents the amplitude of both forces, where ρa is air density. 1 2 1 2 F = ρ AC W~ ,F = ρ AC W~ (II.1) L 2 a L e D 2 a D e

F~ is the traction force of the tether. • trac Kite Choice

To maximize the system’s generated instant power the traction force needs to be max- imized, which means having a high aerodynamic force and a low weight. So in order to use a specific kite in a wind energy exploitation system, it should satisfy the following criteria: Most importantly, it should have a high aerodynamic efficiency, and secondly be light but still be strain, resistant; and easily maneuvered. Being light and strain depends basically on the materials the kite is made up of. Mean- while, a high aerodynamic efficiency and maneuverability, both depend on the kite design, but each has opposite requirements to the other [FMP10]. Hence, a kite designer should find a trade-off between these two. Another important parameter is the kite surface. On one side, the kite’s exploited power is a linear function of its surface [KAB08], and a bigger surface enables the kite to work at higher wind speed, and results in more stability. On the other side, the bigger the kite is, the more difficult it is to be oriented. When first it was suggested, the Laddermill [Ock96] proposed using rigid wings as they are more efficient, but due to safety issues [Ock01], they were soon replaced with flexible light-weighted ones. Suggestions were made to improve flexible kites’ efficiency by using multiple kites on the same tether (or set of tethers). Fig.II.3 shows two proposed struc- tures; the first is to have a stack of kites, as in, for instance, the case of the Laddermill of Delft [LW06]. The second is to link two kites to the end of the same tether, which results in the reduction of the tether drag and the power needed in the recovery phase [HD06]. Both described structures will allow having the same traction force for a smaller space and less land requirements, but are more difficult to be modeled and controlled. For early experiments, commercial kites were used, such as the Clark-y kite (10m2) used 40 II. Relaxation Cycle Systems: Structure and Modeling

Figure II.3: Multiple-kite proposed structures [HD06]. in KiteGEN program [CFM07], the Peter Lynn Guerilla (10m2) Kite used by Worcester Polytechnic Institute (WPI) team [KAB08], and the Peter Lynn Bomba (8.5m2) surf- kite (shown in Fig.II.4) used by Delft team for their small-scale 2kW testing Laddermill [LRO05]. However, research has been going on to design and develop bigger and more specialized kites [Dun14].

Figure II.4: The peter Lynn Bomba kite.

II.2.a-ii Kite Orientation

While power generation is a direct result of pulling the tether out and turning the electrical machine, choosing a kite orbit is important to insure a maximum average power during the kite cycle, while respecting the structural limits of the system, as well as the limits on the controls and state values. In order to operate, the kite must stay in its power zone, a zone where enough lift force is applied on it to keep it flying. The power zone is a half hemisphere, whose center is the point where the kite tether is parallel to wind direction. Fig.II.5 represents this power region. Directing the kite to follow a certain optimal orbit is done through an orientation mech- anism that controls the kite roll angle and/or attack angle, as well as the control of the tether traction. The orientation mechanism may act on the kite tethers starting from the ground, and in this case there are usually 2 or 4 tethers; or it can be up close to the kite, as shown in Fig.II.1, and receiving the control signals from the ground station through wireless connection. In this case, the mechanism’s weight is added to the kite’s. II.2. Kite Generator System 41

Minimum Power

Medium Power

Maximum Power

Risk of falling

Wind direction

Figure II.5: The kite power region.

II.2.a-iii The Tethers

Tethers are needed to transmit the aerodynamic forces acting on the kite to the ground- based generator. Two aspects are important here, the number of tethers, and their design, including their diameter and composition. The number varies usually between one and five tethers. The less the tethers, the more difficult it is to control the kite’s orientation by earth-based controllers. On the contrary, according to [KAB08], using more than one-tether scenario decreases the system efficiency due to their weight and drag force. This has led Delf university team to adopt the one- tether configuration [Ock06][FS12], but did not convince the KiteGEN and WPI team [Bal08]. Instead, they decided to use 2 and 4 tethers respectively, as this allows them to avoid using controllers installed on the kite, which will results in heavier kites, in addition to avoiding disturbances and failures associated with wireless communication between the controllers and the on-ground control unit. Furthermore, tethers should be strong enough to bear high traction, but light and with a small diameter in order to neglect their weight and drag force F~t. The KiteGen team used, for its small scale prototype, 1000m tethers made up of composite materials, Dyneema, that make it as light as similar steel tethers but 8 to 10 times more resistant [Fag09]. It is worth mentioning that Dyneema Company has been devoting an effort to developing tethers specially for the kite-based power systems.

II.2.b KGS Modeling

Many models for the kite and the tether were proposed. They vary in complexity and closeness to reality between the simple point mass model and the finite element implemen- tation [WLRO08]. The point mass model is useful to estimate the possible generated power and is very light to be used in real-time control feedback loops [Die01][CFIM06]. A much more advanced model for the kite is the multi-body model shown in Fig.II.6. In addition to modeling 42 II. Relaxation Cycle Systems: Structure and Modeling

the distribution of the forces acting on the kite, the model takes into consideration the deformation of the kite resulted from these forces. This model, however, is quite computa- tionally costly. A trade-off between the kite point mass model and the multi-body model is the rigid body model: It applies the already developed model equations for aircraft flight dynamics, with the addition of the tether’s resulted forces and moments [GBS10]. The resulted model is simpler to be used in real time operation.

Figure II.6: Presentation of the kite’s multi-body model [WLRO08].

For large scale kite-based systems, the tether model should be considered when controlling the system. A realistic model takes into account the tether weight and drag force and includes its elasticity [BO07][PO06]. In some studies [AHB11a][Die01][CFIM06], the tether’s effect is totally neglected and the obtained model is useful as a base study to estimate the generated power. Rigid-body model for the tether is also used for feedback control and nominal trajectory design. In this model the tether is straight and rigid with a uniform mass and a distributed drag. More complex models discretize the tether into a series of point masses connected by hook joints [WLO07a][Bre11], and may add the effect of the tether elasticity by considering viscoelastic springs added to the hooks [WST08][Bre11]. The later model can be reduced to a simple spring-damper model [GBS10]. Usually two types of modeling are used, a simple model for the control feedback and a more close-to-reality complex one for simulations. In this thesis, the following hypotheses are considered:

A single-point model for the kite and the tether is adopted. Such a model is a rough • one as it ignores the kite flexibility and deformations. It will, however, be used for control purpose and power estimation. II.2. Kite Generator System 43

Figure II.7: Lumped mass tether model [WLO07a].

The tether is inelastic and almost straight. This hypothesis is correct when the • tether’s length is less than 1000m and its inclination is less than 80 degrees [OG08].

Wind is uniform with a non-varying direction, because wind speed at high altitudes • is regular.

The geometry of the tether allows neglecting its lift force, and considering only the • drag Cdt. A high effective aerodynamic efficiency G of the kite and the tether. In this case, • e Ge is introduced in [HD06] by: C G = L (II.2) e Ac CD + 4A Cdt

where A is the kite surface and Ac is the crosswind area of the tether. Kite’s position and velocity as well as the traction force are known throughout the • system’s functioning using observers or sensors. The previous assumptions cannot be applied if the goal is to study the control and the stability of the orientation system. Here, however, the main interest is to study the grid connection part and to estimate the power generated by such a system.

II.2.b-i Kite Dynamics

The kite dynamic model originally developed in [Die01] and used in [CFIM06] is adopted here. As illustrated in Fig.II.8, forces acting on the kite include the gravity force F~grav, aer the aerodynamic force F~ and the tether traction force F~trac. The dynamics can be expressed in the spherical coordinates ~er,~eθ,~eφ as follows: aer m~γ = F~grav + F~ + F~trac (II.3) where m is the kite mass, and ~γ is the kite acceleration expressed in eq.II.4. rθ¨ + 2r ˙θ˙ rφ˙2 sin θ cos θ ¨ ˙− ˙ ~γ = r sin θφ + 2φ(r ˙ sin θ + rθ cos θ) (II.4) r¨ r(θ˙2 + φ˙2 sin2 θ)  −    44 II. Relaxation Cycle Systems: Structure and Modeling

The gravity force is expressed in eq.II.5.

Figure II.8: Kite’s main forces.

sin θ ~ Fgrav = mg  0  (II.5) cos θ −    The aerodynamic force F~aer is related directly to the effective wind We, that is the differ- ence between the wind speed and the Kite’s velocity. Assuming the wind speed Vv is in the direction of x-axis, We is given by eq.II.6.

W V cos θ cos φ θr˙ eθ v − W~ e = W = V sin φ φr˙ sin θ (II.6)  eφ − v −  Wer Vv sin θ cos φ r˙    −      The aerodynamic force has two components, a drag and a lift. In order to express both, a kite related coordinates (~xw, ~yw, ~zw) are defined as follows:

W~e ~xw = is carried on the longitudinal axis of the kite • − |We| ~y is carried on the line connecting the kite’s tips • w ~z = ~x ~y is perpendicular on the kite surface and directed upwards. • w w × w

With these definitions, the drag and the lift components of F~aer are:

F~ aer = 1 ρ AC W 2~x D − 2 a D| e| w (II.7) F~ aer = 1 ρ AC W 2~z L − 2 a L| e| w

The kite related coordinates (~xw, ~yw, ~zw) are transferred to the spherical ones through II.2. Kite Generator System 45

Figure II.9: Kite’s attached coordinates.

p the intermediate coordinates (~er,~ep,~eo). ~ep is the unit vector defined on W~ e , which is the projection of the effective wind on the plane specified by ~eθ,~eφ:

p Weθ W~ e W~ e (~er.W~ e).~er ~ep = p = − p = Weφ (II.8) W~ e W~ e || || || || 0     while: W − eφ ~e = ~e ~e = W (II.9) o r × p  eθ  0   Taking into account eq.II.8 and the fact that the roll angle ψ, shown in Fig.II.10, is the control input, the kite-related coordinate (~yw) is written in the defined intermediate coordinates (~er,~ep,~eo) as follows:

2 W . sin ψ W . cos ψ ~y = sin ψ.~e er .~e + sin2 ψ er .~e (II.10) w r ~ p p v ~ p o − We u − We ! || || u || || t

p 2 2 Wer tan ψ Considering the notations: L = W~ e = W + W , η = arcsin , vecy can be || || eθ eφ L w expressed as: q ~y = sin ψ.~e sin η cos ψ.~e + cos η cos ψ.~e (II.11) w r − p o

Now that the kite-related coordinates (~xw, ~yw, ~zw) are expressed in (~er,~eθ,~eφ), the drag and lift can be written in eq.II.12 and eq.II.13, 1 F~ aer = ρ AC W W~ (II.12) D 2 a D| e| e 46 II. Relaxation Cycle Systems: Structure and Modeling

Figure II.10: Definition of ψ and η angles.

Wer Weφ L [Weφ sin η Weθ cos η] aer 1 1 −Wer − F~ = ρaACL We sin ψ W + ρaACL We cos ψ [W sin η + W cos η] L 2 | | − eθ 2 | |  L eθ eφ  0 L cos η        (II.13) With F~trac = ftrac~er and by developing eq.II.3, the resulted system dynamics can be written as follows: θ¨ = f1(θ, φ, r, θ,˙ φ,˙ r,˙ ψ) φ¨ = f2(θ, φ, r, θ,˙ φ,˙ r,˙ ψ) (II.14) r¨ = f3(θ, φ, r, θ,˙ φ,˙ r,˙ ψ, ftrac)

The coefficients CL,CD are functions of the attack angle α. So the later can be controlled to have a constant coefficients or to increase the system’s efficiency.

II.2.b-ii Machine Applied Traction

The tether traction in the kite F~trac is reduced when transferred to the ground machine. ~ t ~ t This is due to the tether’s weight Fgrav and aerodynamic force Faer. The forces balance in the kite gives: 1 F = mr(θ˙2 + φ˙2 sin2 θ) mg cos θ + ρ A W (C W + C L cos ψ cos η) (II.15) trac − 2 a | e| D er L The forces acting on a segment dl of the tether are the gravity force and the aerodynamic force. Their projections on the tether direction ~er are expressed in eq.II.16. dF t = µg cos θdl grav (II.16) dF t = 1 ρ dC (V V )2dl aer 2 a dt || − L where µ is the mass per length unit. Applying Newton second law on dr gives: 1 dF t = µdrr(θ˙2 + φ˙2 sin2 θ) + µg cos θdr ρ d C (V V )2dr (II.17) trac − − 2 a t || || − L

By integrating II.17 between 0 and r, the reduction in the tether traction Ftrac is calculated; 1 1 ∆F t = µr2(θ˙2 + φ˙2 sin2 θ) + µrg cos θ ρ d rC W 2 (II.18) trac −2 − 2 a t || er hence the traction applied on the on-ground machine is the kite traction of eq.II.15 de- creased by ∆Ftrac. F M = mr 1 µr2 (θ˙2 + φ˙2 sin2 θ) (m + µr)g cos θ trac − 2 − 1 Ac Wer (II.19) + ρaA We CD + C Wer + CLL cos ψ cos η 2" | |
A |We| || h  i II.3. Heaving Point-Absorber System 47

Finally, the system average mechanical energy over one period T is the product of the traction force applied on the machine and tether length variation rate: the radial velocity VL. 1 T P¯ = F M (t)V (t)dt (II.20) M T trac L Z0 As noticed in the average KGS power equation II.20 and the traction force equation II.19, the power P¯M can be written as a function to the radial velocity VL, hence, in order to maximize P¯M , the optimal radial velocity profile should be found.

II.2.c Wind Speed Estimation

When it comes to an HAWE system, it is necessary to estimate the wind speed because of its importance in the optimization and control of the system. This can be measured by having on-board observers, or, since the wind is supposed to be stable at high altitudes, it can be estimated using a wind speed model. Many models are listed in [AJ05], but two are mainly used in the literature [Hus02]. They are expressed in eq.II.21 and eq.II.22.

z γ V (z) = v0( ) (II.21) z0 ln( z ) V (z) = v zr (II.22) 0 ln( z0 ) zr

V (z) is the wind speed at a certain altitude z, v0 is the measured wind speed at an altitude z0, and γ is a friction coefficient that characterizes the surface above which the measurement is done, and can be also described by the roughness factor zr. Using such models, however, is followed by an extremum seeking phase to improve the wind velocity estimation.

II.3 Heaving Point-Absorber System

Among the proposed solutions to extract offshore wave energy is the heaving point- absorber. It captures the up-down wave oscillations and transforms them into a translation movement employed later to generate electricity. In order to harness a maximum of wave energy, the point-absorber oscillations must be controlled to synchronize with the incident wave. This control creates consumption phases that needs to be minimized in order to maximize the overall generated power. The power transformation unit usually rest on seabed, meaning that the captured oscilla- tions should travel a long distance between the floating part and the power transformation unit. A solution to overcome this difficulty is the IPS-OWEC Buoy: A multi-body struc- ture invented by Noren in 1981 and developed by the Swedish company Interproject Service (IPS). In the following paragraphs, the structure and the modeling of a HPS system are consid- ered. The goal of this section is to show the similarity between the HPS and the detailed earlier KGS from a power cycle and a control point of view. 48 II. Relaxation Cycle Systems: Structure and Modeling

II.3.a HPS Structure

A simplified structure of the proposed heaving point-absorber system is shown in Fig.V.1. It consists of a floating object, a buoy, connected rigidly with a tube that transfers its oscillations down to a power transformation unit. A linear gearbox changes the translation of the tube into a rotation motion captured by a synchronous machine. A control of the machine’s rotation velocity insures average power maximization.

Point-absorber

Power Gearbox transformation + Control Power Unit Line Sea Bed

Figure II.11: The HPS simplified structure.

In order to extract a wave’s energy, the PA should generate an opposite wave that interact destructively with the incident one. For this purpose, the PA oscillations and the incident wave must be in phase, and have the same amplitude. According to [McC74], an optimal phase is obtained if the PA frequency spectrum contains the incident wave frequency, hence there is a resonance between the PA and the incident wave. As a conclusion, a bigger PA has a wider frequency spectrum, hence, it will make a better wave generator. Otherwise, the PA should be controlled to expand its spectrum beyond the wave frequencies. The oscillations amplitude can be controlled by modifying a load added to the PA. However, the power that can be absorbed by the point-absorber is limited by two bounds: The optimum destructive interference power defined earlier by eq.I.7: λ ρ(g/π)3 P = E = H2T 3 A 2π w 128 and the Budal’s upper limit [Fal07] for point-absorber in open sea: πρg VH P = (II.23) B 4 T where V is the heaving buoy submerged volume. These bounds define a region of the can-be-extracted wave energy, it is shown in Fig.II.12. As can be noticed from eq.II.23, II.3. Heaving Point-Absorber System 49

in order to increase Budal limit, the point-absorber dimensions should be bigger. On the other hand, they must be much smaller than the incident wavelength in order to neglect the reflection and the refraction phenomena that will be explained in the next section.

Figure II.12: The upper bound of the possible absorbed energy from a sinusoidal wave.

II.3.b HPS Modeling

When considering a body floating in a fluid, waves experience the following phenomena:

Interference: is the superposition of waves traveling in the same fluid. It can be • constructive or destructive.

Reflection: It happens when waves bounce back from an obstacle. • Refraction: It is the deflection of a wave when it passes between two environments. • Diffraction: It considers the obstacle itself as a source of waves during the propaga- • tion of the incident wave.

Radiation: It is creating waves in the fluid due to the floating body motion. • The interference is not taken into account as it does not affect the movement of the body. The reflection and the refraction phenomena are negligible if the floating body dimensions are small compared to the incident wavelength. The remaining phenomena, the radiation and the diffraction, are the ones allowing the PA to absorb the incident wave energy.

II.3.b-i Hydrodynamics Study

As a first step into modeling the HPS, a general case of a floating body with six degrees of freedom is considered (Fig.II.13). It is then simplified to obtain the model in the case of a system with only one degree of freedom. 警欠建健欠決【鯨件兼憲健件券倦" 詣欠決撃件結拳 迎劇詣欠決" 穴鯨鶏畦系継" 茎欠堅穴拳欠堅結" 硬追勅捗 " 経欠建欠 劇剣堅圏憲結 眺 鯨件訣券欠健嫌 計件建結"警剣穴結健" 系 " "劇堅欠券嫌血結堅" 継兼憲健欠建件剣券 建堅結欠建兼結券建 劇結嫌建 憲嫌件券訣 " 硬 欠券穴 劇結嫌建 "稽結券潔月" 劇系鶏エ 荊鶏" 警鶏系劇" "潔剣券穴件建件剣券件券訣 稽結券潔月 鶏堅剣建剣潔剣健結嫌 鶏 系剣券建堅剣健" "

畦エ 経 経エ 畦

50 II. Relaxation Cycle Systems: Structure and Modeling

茅 帖寵暢 系 " 経系警 畦系エ 経系 In the fluid mechanics, Navier-Stokes equations系剣券建堅剣健 (II.24潔剣券懸結堅建結堅,II.25) are employed to find the average extracted power from waves [Bel90]. 系帖寵暢 帖寵暢 硬追勅捗 " % ∂(ρ)弔 劇剣堅圏憲結 系 ┸硬+ (ρV ) = 0 (II.24) 眺 よ 系 " 継兼憲健欠建剣堅 ∂t ▽ %弔 dV 弔 ρ = P + µ系 ┸硬2 V + ρB (II.25) dt − ▽ ▽ エ where ρ is water’s density, P is the pressure,鶏警鯨警B is the fluid経系 external 畦系 acceleration, µ is the 硬帳" 系剣券建堅剣健 潔剣券懸結堅建結堅 fluid viscosity coefficient, and V is the fluid velocity field. Eq.II.24 represents the fluid continuity, and eq.II.25 is the momentum balance equation. Noticeably, these equations are nonlinear, as they contain the total derivative of the fluid velocity field V .

倦屎王

ぬ に は 卒王 の な

穴嫌 ね 続王 Figure II.13: Cartesian券屎王 coordinates linked to a floating body with 6 degrees of freedom.

For the sake of simplicity, the following hypotheses are considered:

Incompressible fluid: the fluid density is constant, thus the fluid mass is conserved. • Irrotational flow V = 0: This allows to write V as a scalar potential φ = V . • ▽x ▽ Non viscous fluid: Which allows to neglect the forces related to fluid viscosity (µ = 0). • H << 1: In this case, the nonlinear terms of the total derivative are negligible. • h Sinusoidal-nature waves: the wave (A) is written as the multiplication of two terms: • a function of position, and another of time.

A = a(x, y, z)ejwt (II.26)

where a(x, y, z) describes the position in a Cartesian coordinate (Fig.II.13), and 1 w = 2πT is the wave pulsation. By considering these simplifying hypotheses, eqs.II.24, II.25, are written as follows:

2 (φ) = 0 (II.27) ▽ ∂V P = ρ( + gz) (II.28) ∂t The potential φ that satisfies eqs.II.27,II.28 needs to be found in order to calculate the forces and the moments acting on the floating part of the system, thus to find the extracted II.3. Heaving Point-Absorber System 51

power. For a sinusoidal-nature wave the diffraction and the radiation phenomena are de- coupled, and the total potential φ can be written as a superposition of each phenomenon’s potential added to the wave proper potential φI :

φ = φI + φD + φR (II.29)

Where φD is the diffraction scalar potential and φR is the radiation scalar potential. In addition to the continuity equation (eq.II.27), the potentials have to satisfy boundary conditions. Once found, φ is used to calculate the pressure in eq.II.28, thus the forces Fex and the moments M acting on the system as in eq.II.30.

F = ~nP ds ex S (II.30) M = (~r ~n)P ds RRS × where ~n is the unit normal vector on theRR floating body surface, S is the body’s surface; and ~r is the unit rotational vectors around (x, y, z)(see Fig.II.13). In the search of a solution for eq.II.27 and eq.II.30 in the case of one degree of freedom, that is a translation z, two cases are distinguished: Regular and irregular waves.

Regular Waves

As mentioned earlier, a regular wave is purely sinusoidal with a specific amplitude H and period T . In this case, from eq.II.30, the hydrodynamic excitation force is:

Fex = (m + mr)¨z(t) + Rrz˙(t) + Cz(t) (II.31) where m is the floating body mass, mr is the added mass, Rr is the radiation damping coefficient; and C = ρ g S with S being the sectional surface. ∗ ∗ Eq.II.31 can be represented using an electrical approach, in which (m + mr) is an induc- tance, Rr is a resistor, C is a capacitor,z ˙(t) is the current; and Fex represents the voltage. Accordingly, the average power extracted from the system is: 1 P = R vˆ2 (II.32) av,reg 2 r withz ˙(t) := v(t) =vcos ˆ (wt + ψ)

Irregular Waves

An irregular wave is, as shown in Fig.II.14, the superposition of regular waves with random amplitudes and periods. The sea surface elevation in the case of irregular waves is:

∞ jwnt Z(t) = Aˆne (II.33) n=1 X The magnitude Aˆ and the period T = 2π are random variables with Normal distribution. n n wn

When a linear system has a sum of independent random variables as an input, its output 52 II. Relaxation Cycle Systems: Structure and Modeling

Figure II.14: An irregular wave is the superposition of regular waves with random amplitudes and periods. is calculated using the inputs’ power spectrum [Fal02]. From eq.II.31, the system velocity power spectrum for the case of irregular waves and a sea state (i), is given by:

S (w) = G(w) 2 S (w) (II.34) vi | | Zi where G(w) is the relation between the velocity and the position depending on w. Again, from [Fal02], the amplitude of the system velocity can be found by applying the inverse Fourier transformation: −1 vˆ = TF [Svi(w)] (II.35) and the average power in the case of irregularp waves is: 1 P = R TF −1[ G(w) 2 S (w)] (II.36) av,irr 2 r | | Zi II.3.c Power Maximization Techniques

Now that the average power expression is found for both, regular and irregular waves, techniques to maximize it are discussed. Among the various used methods, three are presented here. The optimal amplitude control, which acts on the parameter Rr, the optimal phase control that controls the phase between the floating body and the wave; and finally a combination of both previous methods, called the reactive control.

II.3.c-i Optimal Amplitude Control

From an electric point of view, this method aims at finding a tuning value RPTO (Power Take Off) that can be added to Rr in eq.II.31, in order to maximize the extracted power expressed in eq.II.32. In the frequency domain, eq.II.31 is written as: wZ(w) 1 = C (II.37) Fex(v) (m + m )w + j(R + R ) w − r r PTO Thus, 1 RPTO Pav = Fˆex(w) (II.38) 2 ( C (m + m )w)2 + (R + R )2 w − r r PTO The optimal value of RPTO verifies the condition, ∂ ∂R (Pav) = 0 PTO ⇒ (II.39) Rˆ = R2 + [(m + m )w C ]2 PTO r r − w q II.3. Heaving Point-Absorber System 53

and the corresponding obtained power is

1 Fˆex(w) Pav = (II.40) 4 R + R2 + [(m + m )w C ]2 r r r − w q II.3.c-ii Optimal Phase Control

Corresponding to the same electric analysis, extracted power can also be maximized by synchronizing the force (voltage) Fex and the velocity (current) v, which means: C (m + m )w = 0 (II.41) r − w This condition is independent from the type of the wave energy system. It can be achieved by applying a latching control, as proposed in [BDC04], [FJH09] and [Fal02]. The control blocks the floating body for a suitable time interval, then let it go when it arrives to the optimal phase position. Another proposed method, though too complicated to be used, is adding a controllable mass msup to the floating object in order to have: C C (m + m + m )w = 0 mˆ = (m + m ) (II.42) r sup − w ⇒ sup w2 − r The corresponding average power is: ˆ2 1 RPTOFex Pav = 2 (II.43) 2 (Rr + RPTO)

II.3.c-iii Reactive Control

A combination of the two previous methods is the so-called reactive control. It is called reactive because the system reacts to each sea state by applying the suitable controls that maximize the extracted power. For the case of regular waves, the extracted power using a reactive control is the result of combining eq.II.40 and eq.II.43, which is ˆ2 1 Fex Pav = (II.44) 8 Rr For irregular waves it is impossible to define power maximization conditions for each frequency in the spectrum. A proposed solution is to optimize the parameters for the frequency where the power spectrum is at its maximum.

II.3.c-iv Comparison

The explained control methods are compared using Matlab for both regular and irregular waves. The testing floating body is a cylindrical one with a radius r = 2m and a height L = 1m. It is assumed to be completely submerged and balanced. The body’s mass is m = ρ(πr2)L = 1.291 104 kg. The parameters F , m ,R ,C of × ex r r this object are calculated using WAMIT software. They are functions of the wave period. Fig.II.15 shows the variations ofthe radiation parameter Rr and the added mass mr as a function of wave’s period. C’s variations with frequency are neglected:

C = 1.264 105 × 54 II. Relaxation Cycle Systems: Structure and Modeling

Figure II.15: Floating body parameters, added mass mr and radiation parameter Rr.

In addition to the wave frequency, the excitation force Fex is a function of the wave amplitude H. Its variations are shown in Fig.II.16.

Figure II.16: The resulted excitation force as a function of the wave parameters.

At first, the waves are considered to be regular. For a wave (H = 1.25m, T = 6.5sec), the profiles of power generated using each power maximization methods are compared. As noticed in Fig.II.17, the power generated using an optimal phase control is as high as that generated when applying a reactive control, and both generate almost 16 times the power generated using an optimal amplitude control. In the case of irregular waves, waves are considered as a superposition of regular waves with random amplitudes and periods (eq.II.33). As seen earlier, in the case of irregular waves, the power spectrum is used to choose the suitable controls. Jonswap spectrum is adopted here [BTDB10]. It is the (Joint North Sea Wave Project) spectra that is an empirical approximation of the power distribution with respect to waves frequency:

f −5 pi 4 2 4 −5 β [ 4 ( f ) ] 2 SZi = αHsifpif γ e (m s) (II.45) where Tpi = 1/fpi and Hsi are the wave period and amplitude respectively for a certain sea state, γ = 3.33 is the scaling factor, and α, β are given by II.3. Heaving Point-Absorber System 55

Figure II.17: Comparing generated Power in the case of a regular wave (H = 1.25m, T = 6.5sec).

f−f [− pi ] σ2f2 0.0624 2 pi α = 0.185 , β = e 0.23+0.336γ− 1.9+γ with

0.07f < f σ = pi 0.09f f ( ≥ pi The average power in this case is written by:

∞ P = R H(w) 2 S (w)dw (II.46) av,irr PTO | | Zi Z0 For example, the empirical approximation for the sea state of Fig.II.14 is given by the curve in Fig.II.18.

Figure II.18: Jonswap spectrum of wave in Fig.II.14.

Considering the set of sea states in Table II.1, the average power is calculated for each state using eq.II.46 and maximized via optimal amplitude control and reactive control. Fig.II.19 compares the resulted average power in the case of regular and irregular waves. Using reactive control certainly increases the power efficiency. The increment is more significant in the case of regular waves. As shown in Fig.II.20, comparing the produced energy without control, using a latching control and applying an optimal reactive control shows that even though in the case of 56 II. Relaxation Cycle Systems: Structure and Modeling

Table II.1: Test sea states

State Hs(m) Tp(sec) 1 0.25 4.8 2 0.5 4.8 3 0.1 4.8 4 1.5 6.4 5 2.0 6.4 6 2.5 8.4 7 3.5 8.4 8 3.5 9.2

Figure II.19: Average power for regular (marked line) and irregular waves by applying reactive and optimal amplitude control. optimal control the system has consumption phases periodically, the overall generated energy is greater than that obtained without using a control or using a latching control. The output power profile of the system in this case is similar to that of the KGS system discussed earlier in sec.II.2. Hence, from a grid integration point of view, both systems can be handled in the same way.

Figure II.20: Absorbed energy without phase control (lower broken curve), with latching phase control (fully drawn curve) and with theoretically ideal optimum control (broken wavy curve). The curves show the wave energy (in joule) accumulated during 5 seconds.

II.4 Conclusion

In this chapter, two relaxation-cycle renewable energy systems were presented and mod- eled. Those are the kite generator system (KGS) which is a kite-based traction system that II.4. Conclusion 57

aims to harness high altitude wind energy, and the heaving point-absorber system (HPS) which is basically a floating body that captures sea waves oscillations and transforms them to a rotary movement employed to produce electricity. We have to make a choice to conduct research on the maximization of harvested power. The kite generator system is more complex due to its multidimensional behavior: 3D in space for the kite and a torque/speed couple for the ground electric machine. The obtained KGS models will be used to build and test controllers to control the kite’s orientation and estimate its traction force and radial velocity.

Chapter III Kite Generator System: Supervision

Contents III.1 Introduction ...... 61 III.2 Nonlinear Model Predictive Controller ...... 62 III.2.a Methodology ...... 63 III.2.b Application ...... 67 III.3 Virtual Constraints-based Controller ...... 71 III.3.a Methodology ...... 75 III.3.b Application ...... 80 III.4Conclusion ...... 83

Abstract

The KGS control can be divided into two coupled parts, the kite orientation and the ground-based electric machine control. Simply stated, the kite orientation mechanism controls the roll angle of the kite, while driving the machine controls the tether radial velocity. This chapter is dedicated to presenting the KGS orbit optimization and tracking. Two control methods are investigated: A nonlinear model predictive controller (NMPC) and a virtual constraints-based control (VCC). The NMPC was already applied and tested, and it showed good results. It underwent a lot of research as well to improve its efficiency for real-time application. The second method, the VCC, is a novel application of virtual constraints used in robotics control and the primer study presented here shows its potential to achieve orbit tracking via a simplified approach. The control strategy based on these controllers is built and tested through simulations.

III.1. Introduction 61

III.1 Introduction

Generally, a kite-based system control should, on one hand, ensure the kite’s (or kites set) tracking of certain orbits that respect the systems constraints and maximize the generated average power, and, on the other hand, manage the power generated/consumed by the system. The reference trajectory generation is usually done either by choosing an eight-shaped orbit and optimizing its period and velocity to have a maximum power generation, as suggested by Argatov [AS10a], and used in [IHD07] and [WLO07a]; or by maximizing the generated power directly while following an imposed eight-shaped path that respects the state constraints as KiteGEN team has done [FMP10]. A general model of the system has the form,

x˙(t) = f(x(t), u(t),P (t)) (III.1) with constraints on the state x(t) and the control vector u(t),

x x(t) x , u u(t) u (III.2) min ≤ ≤ max min ≤ ≤ max The state vector x(t) contains information on the kite’s position and velocity, usually presented in the spherical coordinates (r, θ, φ). Meanwhile, the control vector u(t) may contain controls of the kite’s different angles: roll, yaw and attack, in addition to control of the tether length variation rate. As for P (t), it contains all the external effects that influence the system behavior, e.g. wind perturbations and grid voltage dips. Depending on the system design and the measurement sensors, the control strategy is built. Measuring the state vector can be done through use of observers or sensors such as GPS receivers, Gyro sensors connected to the ground control unit through wireless communi- cation, and on-ground traction force and inclination angle measurements. The mentioned constraints include:

The kite flying in a limited area and avoiding being crashed. • Not exceeding a certain velocity or lift force that is specified by the kite’s and tether’s • properties and respects the ground-based electric machine limits.

Constraints on the control variables and their changing rates. • As the kite-based system is nonlinear, constrained, and unstable in the open-loop, an equally complex sophisticated autonomous control strategy should be applied, with a suf- ficiently small sampling time to insure the tracking of any possible disturbance. A simple linear control [WLO07a] is not suitable to control such a system as it cannot handle disturbances and is only efficient around the linearizing point. A nonlinear model predictive control (NMPC) was proved to be convenient to generate the needed controls for trajectory tracking, though [BO11] doubted the performance of this method because it leads the solution to converge to different local optima depending on the initial conditions and consumes a lot of memory when it comes to application. Still NMPC was used in [IHD07], [AHB11b], and for real time application a Fast NMPC was proposed and tested 62 III. Kite Generator System: Supervision

by KiteGen team [CFM10]. Neural network control [FH07] has demonstrated promising results in applying a robust tracking of the kite trajectory facing severe wind disturbances. Meanwhile, J. Baayen and W. Ockels have suggested a one-dimensional representation of the trajectory that allows the transformation of the trajectory tracking problem to single-input single-output (SISO) problem and used a nonlinear adaptive control to achieve the trajectory tracking [BO11]. Other suggested trajectory tracking methods include direct-inverse control [NFM11] and robust control [PO07b]. In this chapter, two methods to control the system are proposed. The first uses a nonlinear model predictive controller (NMPC), a method that was already applied and tested and it showed good results in this domain. The second approach is a novel one investigated and proposed in this thesis. It is called: Virtual constraints-based control (VCC). The methodology of using both controllers and their application via simulations is presented in the following sections.

III.2 Nonlinear Model Predictive Controller

Model predictive control (MPC), also called receding horizon control, is a multi-variable control based on iterative finite horizon optimization.

As shown in Fig.III.1, at an instance t, the current control action ui is obtained by solving numerically an optimal control problem on a finite time horizon [t, t + T ]. The control problem is constrained by limits p on the system, the control and the state measurement. { }i It uses the current state xi as the initial state and yields an optimal control sequence u (t), u (t + t ), ...., u (t + T ) in which t is the calculation step. The first control { i+1 i+1 s i+1 } s ui+1(t) is applied to reach the next state xi+1. The calculations are repeated starting from the new state to find the next control action and a new prediction path under the new constraints set p . { }i+1 To sum up, the principle elements of the MPC method are:

An internal dynamic model of the controlled system. • A history of past control moves. • An optimization cost function J over the prediction horizon. • A set of constraints on the optimization algorithm. • MPC strategies were successfully employed in thousands of industrial applications, such as petrochemical industry and aerospace and car industry. MPC takes into account ac- tuators limitations, and operates close to constraints, as well as it has the possibility to adapt easily to changes in the system and its constraints. A nonlinear model predictive control (NMPC) considers a nonlinear model for the predic- tion function and nonlinear constraints. It adds to linear MPC a new complexity which is the non-convexity of the optimal control problem, which poses challenges for NMPC’s stability and numerical solution. III.2. Nonlinear Model Predictive Controller 63

Figure III.1: Illustration of model predictive control output.

The numerical solution of the NMPC optimal control problems is typically based on direct optimal control methods, using Newton-type optimization schemes. They can make use of the fact that consecutive optimal control problems are similar to each other, hence ini- tialize the Newton-type solution procedure efficiently by a suitably shifted guess from the previously computed optimal solution, saving considerable amounts of computation time, and permitting real time iterations.

III.2.a Methodology

In the next paragraphs, an NMPC-based control strategy is proposed to control the KGS system. It can be summarized by the following steps:

Choosing primary eight-shaped orbit parameters. • Optimizing the parametric orbit by maximizing its generated power. • Finding the 3D time dependent trajectory. • Applying an NMPC to insure trajectory tracking • Those steps are detailed in the following sections.

III.2.a-i Primary Orbit Choice

The initial kite orbit to be optimized is characterized by the tether’s initial length r0, and the parameters defining θ’s and φ’s variations space: ∆θ, ∆φ, θ0, φ0 and Rot (see Fig.III.2). The trajectory is expressed by the parametric equations:

θ(τ) = θ + cos(Rot)∆θ sin(2τ) sin(Rot)∆φ sin(τ) 0 − (III.3) φ(τ) = φ0 + sin(Rot)∆θ sin(2τ) + cos(Rot)∆φ sin(τ) 64 III. Kite Generator System: Supervision

$

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Figure III.2: Initial orbit parameters.

The primary trajectory parameters determine the maximum wind power that can be ex- ploited by the KGS. The bigger the values of ∆θ, ∆φ are, the bigger the orbit and the more average generated power is. Further more, the generated power increases with the orbits rotation angle Rot. The choice of the other parameters θ0, φ0 is dependent on the wind direction. These dependencies will be illustrated later in the discussion presented in sec.IV.4.d.

III.2.a-ii Orbit Optimization

The optimization phase aims at finding the radial velocity profile and the orbit’s period that maximizes the produced average power during one cycle of the system, hence finds the maximum power cycle. In order to do so, both the produced power and the closed orbit condition are expressed as functions of the dimensionless variable τ. Remember that the system average mechanical power over one period T is:

1 T P¯ = F c,trc(t)V (t)dt (III.4) M T L Z0 c,trc where F is the traction force acting on the tether, and VL is the tether radial velocity. According to [AS10a], by changing the integral time variable t [0,T ] to the dimensionless ∈ parameter τ [0, 2π], and making use of the substitution V (t) = V v(τ), eq.III.4 can be ∈ L expressed as follows: 1 P¯ (v) = ρ AC G2V 3J (v) (III.5) M 2 a L e 0 where V is the wind speed amplitude and J0 represents the normalized average power P¯M 2 3 [ARS09], with the normalizing coefficient being: ρaACLGeV . J0 is expressed by eq.III.6.

2π 0 (w|| v)vh(τ)dτ J0(v) = − (III.6) 2π h(τ) dτ R 0 w||−v R 2 2 2 with h(τ) = dθ + dφ sin (θ) and w|| = sin(θ)cos(φ). When the attack angle α is con- stant, the aerodynamicp coefficients are constant. III.2. Nonlinear Model Predictive Controller 65

The aerodynamic efficiency Ge can however be controlled in order to improve the perfor- mance of the system. Eq.III.7 represents a possible functionality of this coefficient to the attack angle. CL = CL0 + CLαα C = C + K C2 (α) (III.7) D D0 ∗ L G = CL e CD where α is written as a linear function of the w|| and its variations can be optimized when joined to the average mechanical power expression of Eq.III.5.

α(τ) = a w (τ) a (III.8) 0 ∗ || − 1 α α a = max − min 0 w w ||max − ||min αmaxw||min αminw||max a = − 1 w w ||max − ||min

Orbit optimization aims at having a high crosswind speed, in order to develop a high traction force and thus higher power production. The crosswind speed is expressed by:

W p = G V (w v) (III.9) | e | e || − This means the optimal tether radial velocityv ˆ(τ) should be found. This velocity maxi- mizes the produced power that was presented earlier by eq.III.6, and satisfies the closed T loop orbit condition 0 VL(t)dt = 0, which is expressed by: [ARS09] R 2π vh(τ) dτ = 0 (III.10) w v Z0 || −

Once found,v ˆ(τ) is used to derive the traction force given by: [AS10a] 1 f = ρ AC G2V 2(w vˆ)2 (m + m )g cos θ (III.11) trac 2 a L e v || − − t

III.2.a-iii Orbit Period

All done calculations and variables are functions of the dimensionless parameter τ [0, 2π]. ∈ The orbit’s time period T and the relation between the time variable t [0,T ] and τ need ∈ to be defined. The period equals the orbit length divided by the kite’s speed: dl T = (III.12) r˙ I | | With dl a differential length along the orbit:

′ ′ ′ dl~ = dr~er + rdθ~eθ + r sin θdφ~eφ = (r ~er + rθ ~eθ + r sin θφ ~eφ)dτ = ~rdτ˙

The velocity vector ~r˙ at a certain point of the orbit is carried on its tangent:

dl~ r′~e + rθ′~e + r sin θφ′~e ~t(τ) = = r θ φ dl 2 k k r′2 + r2 θ′2 + φ′2 sin θ q "
66 III. Kite Generator System: Supervision

It can be decomposed into two components:

′ ′ ′ ′2 ′2 2 θ ~eθ + sin θφ ~eφ ′ ~r˙ = r ~er + r θ + φ sin θ = r ~er + ~r˙⊥ t~⊥ θ′2 + φ′2 sin2 θ | | q and this can be written as: p

′ ′ ′ r ~er + r(θ ~eθ + sin θφ ~eφ) ~r˙ = ~r˙⊥ | | r θ′2 + φ′2 sin2 θ the effective wind tangent component is: p

W p 2 = W~ ~r˙ 2 = W~ 2 + ~r˙ 2 2 ~r˙ (W~ .~t ) | e | | ⊥ − ⊥| | ⊥| | ⊥| − | ⊥| ⊥ ⊥ 2 By adding and subtracting (W~ ⊥.~t⊥) ,

2 p 2 2 ~r˙ = W~ .~t + (W~ .~t ) + We W~ (III.13) | ⊥| ⊥ ⊥ ⊥ ⊥ | | − | ⊥| q p Due to the crosswind motion law We = G (V r˙) and putting Ω = W~ .~t , eq.III.14 | | e || − ⊥ ⊥ ⊥ is written as: ~r˙ = W~ .~t + Ω2 + G2(V r˙)2 W~ 2 (III.14) | ⊥| ⊥ ⊥ ⊥ e || − − | ⊥| q Eq.III.12 gives: [AS10a] r θ′2 + sin θφ′2 T = dτ (III.15) ~r˙ I p | ⊥| The quantity Ge has a high value; therefore, the mathematical model of wind energy generation can be further simplified to:

~r˙ | ⊥| = ω + ω2 + G2(w v)2 ~w 2 = G (w v) V ⊥ ⊥ e || − − | ⊥| e || − q Hence, the period can be finally expressed in eq.III.16.

2π r(τ)h(τ) T = dτ (III.16) G (w (τ) v(τ)) Z0 e || − and the time vector is given by:

τ r(σ)h(σ) t = dσ (III.17) G (w (σ) v(σ)) Z0 e || − III.2.a-iv NMPC Design

Now that the optimal tether’s radial velocity and the period corresponding to a given eight-figured orbit are found, the nonlinear model predictive control is applied to achieve tracking of the generated orbit while respecting the system’s constraints. This is done via control of the kite roll angle and the tether’s traction force, in addition to the attack angle if the aerodynamic efficiency is optimized as well. The resulted kite orbit is a three-dimensional orbit described in the spherical coordinates by r(t), θ(t), φ(t). Orbit tracking is divided into: III.2. Nonlinear Model Predictive Controller 67

Kite orientation via the control of its roll angle to follow the reference (x, x˙): x = • (θ, φ)

Tether’s radial velocity control by driving of the PMSM rotation velocity (V = • L Ωs/K).

At every time step,x ¨ that minimizes the cost function of eq.III.18 is calculated and con- trolled by the roll angle ψ. The chosen cost function reflects the distance from the reference orbit. f = (¨x x¨) + λ (x x) + λ (x ˙ x˙) 2 (III.18) k ref − 1 ref − 2 ref − k where λ1, λ2 determine how quickly the state converges to the reference orbit. Fig.III.3 summarizes the KGS proposed NMPC-control strategy. It starts from the para- metric initial orbit and generates an optimal time-dependent orbit. An NMPC is applied to find the roll angle that achieves tracking of (θ(t), φ(t)), while the radial velocity control is insured by controlling the ground machine rotation velocity.

! ! ! ! ! #"%! INCO $5/,27(7/32 ! !3275300,5 ",*.(2/61 ! HNGO ! ! ! NF;H;F! M; HMONCO ! ! ! ! NF;H;FM; HMONGO M ! ! ! $5)/7 NF;H;F; HMONGO '5(26-,5 73 "(*./2, K 6/+, $47/1/:(7/32 '/1, +31(/2 > !328,57,5 !327530 DLNGO E NCO FNGO! ! %(5(1,75/* $5)/7 &967,1 %(5(1,7,56 @;?;A;BJ; = < Figure III.3: NMPC-based control strategy.

III.2.b Application

As mentioned earlier, choosing the primary orbit to be optimized is an essential step in determining the maximum possible extracted average power, and the ratio between the average and the maximum power, or what we choose to call “Performance”. Table.III.1 shows the KGS parameters. The wind velocity is assumed to be constant and regular with a speed V = 4m/s. Fig.III.4 shows the test orbits. Test orbits 2 and 3 result from amplifying the reference test orbit 1, while orbits 4 and 5 result from rotating the reference orbit 30 and 90 degrees respectively.

o Table.III.2 shows the characteristics of the five chosen test orbits with θ0 = 55 and o φ0 = 0 , as well as the estimated corresponding mean power, performance, and the orbits’ period. In [AS10b], it was demonstrated that a bigger trajectory corresponds to greater average power; furthermore, a bigger rotation of the orbit leads to more average power which agree with the results obtained and displayed in Table.III.2. As noticed, the performance gets better as well, because a bigger orbit allows the kite recovery phase to occur further from 68 III. Kite Generator System: Supervision

Table III.1: Kite generator system parameters

R 0.3 Rotor Diameter (m)

Ωmax 25 Maximum rotor rotation velocity (rd/sec) Γmax 22 Motor maximum torque (N.m) m 2.5 Kite mass (kg) A 5 Kite area (m2) 3 ρa 1.2 Air density (kg/m ) CL 1.5 Lift coefficient CD 0.15 Drag coefficient Ts 0.1 Sampling time (sec)

the center of the power region; hence, consumes less energy. The size, however, is a pa- rameter to be optimized according to the system’s location.

Figure III.4: Test orbits: Reference orbit (1) in continuous line, amplified orbits (2,3) in dotted line, and rotated orbits (4,5) in dashed line.

The orbits optimization results in the normalized parametric radial velocityv ˆ which de- pends on the wind direction and the parametric orbit. The time dependent radial velocity profile is found after calculating the orbit period and time vector (eq.III.16,eq.III.17). The resulted profiles in the case of orbits 1, 2 and 3 are shown in Fig.III.5. Notice that the optimal velocity has double the calculated period, so during one orbit two traction and two recovery phases occur. This means doubling the resulted power profile and decreases its continuity. The upper plot of Fig.III.7 shows the KGS energy profile for the orbits 1, 2 and 3. Fig.III.6 shows the radial velocity profiles for orbits 4 and 5 compared to the reference orbit 1. Rotating the orbit results in more average generated power and increases the performance without the need to increase the orbit size or changing the system parame- ters. Contrary to the case of 0o rotation, a 90o rotated orbit preserves the orbit period, which means only one traction and one recovery phase during the orbit. This can be also observed by the energy profiles shown on the lower plot of Fig.III.7. As noticed, the KGS will offer a very high adaptivity, as its rated power can be modified III.2. Nonlinear Model Predictive Controller 69

Table III.2: Testing orbits parameters and optimized orbits’ period, mean mechanical power and performance

Orbit 1 2 3 4 5 ∆θ 10o 20o 20o 10o 10o ∆φ 20o 20o 40o 20o 20o Rot 0o 0o 0o 30o 90o Period (sec) 35.4 59.0 78.4 35.4 35.0 Mean power (W ) 240 732 844 398 840 Performance 0.058 0.094 0.108 0.058 0.100

Figure III.5: Normalized and time dependent radial velocity in upper and lower figure respectively. Reference orbit (1): continuous, orbit (2): dotted, orbit (3): dashed. by changing the kite orbit size and/or rotation. It can also be modified by changing the orbit inclination θ0, or the altitude at which the kite is flying for example. Fig.III.8 shows how the KGS generated average power changes as a function of the kite surface A, the orbit rotation angle Rot, and the orbit inclination θ0. The NMPC controls the kite to follow the generated reference orbit while respecting the state and control constraints. Those are usually imposed by the area the system is flying in and the flight angle’s limits. Assuming the kite flight is limited only by the ground and the tether length, the following constraints are applied:

θ = 30o θ θ = 90o min ≤ ≤ max φ = 90o φ φ = 90o min − ≤ ≤ max r = 90 m r r = 110 m min ≤ ≤ max r˙ = 83.3 m/sec r˙ r˙ = 83.3 m/sec min − ≤ ≤ max ψ = 20o ψ ψ = 20o min − ≤ ≤ max ψ˙ = 4o/sec ψ˙ ψ˙ = 4o/sec min − ≤ ≤ max

Fig.III.9 shows the orbit tracking by applying the already explained optimal predictive 70 III. Kite Generator System: Supervision

Figure III.6: Normalized and time dependent radial velocity in upper and lower figure respectively. Reference orbit (1): continuous, orbit (4): dotted, orbit (5): dashed.

Figure III.7: KGS energy generation. Reference orbit (1): continuous. Upper plot: orbit (2) energy profile in dotted line, orbit (3): dashed. Lower plot: orbit (4) energy profile in dotted line, orbit (5): dashed. control in the case of the first orbit. Here the radial velocity, hence the tether length, is assumed to be controlled by the ground machine as will be shown in the next chapter. III.3. Virtual Constraints-based Controller 71



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Figure III.9: Tracking orbit 1 using optimal predictive control

III.3 Virtual Constraints-based Controller

In this section, the KGS periodic target motion is ensured by a state feedback control law based on virtual constraints approach. The proposed motion planning strategy is a fast in-loop control method that is robust against disturbances and guarantees an exponential orbital stabilization. Virtual constraints (VC) are dynamically enforced relations between a mechanism’s links in order to decrease its degrees of freedom. They coordinate the movement of all links by controlling a single variable. Virtual constraints have emerged recently as a valuable tool to solve motion control prob- lems. This notion has been useful to design controllers for biped robots, as well as, control of underactuated 3DOF helicopter movement [WMS10], pendubot [FRSJ08], and cart- pendulum system [SPCdW05]. Fig.III.10 presents some control problems that were solved using VC. For an under-actuated Euler-Lagrange system, VC are defined as relations among the sys- 72 III. Kite Generator System: Supervision

3DOF helicopter Pendubot

Bicycle Cart pendulum Rabbit Robot

Figure III.10: Some motion and balance control problems solved using VC. tem’s variables and are enforced by feedback. The goal of the feedback design is either to render an existing periodic motion orbitally stable or to force the system dynamics to generate a new periodic motion and ensure its orbital stability [SCdW03][CdW04]. Considering the non-linear Euler-Lagrange system : d ∂L ∂L ( ) = B(q)u (III.19) dt ∂q˙ − ∂q Where:

q is the generalized coordinates vector. • q˙ is q’s velocity vector. • u is the independent control inputs vector. • B is the control matrix. • L(q, q˙) = T (q, q˙) V (q) is the Lagrangian, that is the difference between the kinetic • 1 T− energy T = 2 q˙ M(q)q ˙, where M is a positive definite matrix of inertia, and the potential energy of the system V .

Suppose that this system has n degrees of freedom controlled via n 1 inputs; it is then − under-actuated. dim(u) < dim(q) In this case, n 1 virtual constraints can be imposed on the system’s generalized coordi- − nates as follows: q1 = Φ1(qn)  q2 = Φ2(qn)  . (III.20)  .  qn−1 = Φn−1(qn)    III.3. Virtual Constraints-based Controller 73

and the system III.19 can be reduced to an auxiliary input-free system with a limit cycle:

α(θ)θ¨ + β(θ)θ˙2 + γ(θ) = 0 (III.21)

def where θ = qn and α(θ), β(θ), γ(θ) are scalar functions of θ. This equation represents also the zero or the reduced dynamics of the system. The next example clarifies the virtual constraints approach.

Example: A two-joint robot arm has two DOF: two rotations q1, q2. Controlling the arm’s free end to move along a vertical axis implies forcing the virtual constraint of eq.III.22 that couples both rotations.

l q = Φ(q ) = q arcsin 1 sin(q ) (III.22) 2 1 1 − l 1  2  and can be expressed as well in the form:

y = q Φ(q ) = 0 (III.23) 2 − 1 Since we are seeking a periodic motion stabilization of the kite generator system, the

Figure III.11: Example of a virtually constrained Two joint arm.

VC approach seems a suitable one. In the following paragraphs, the constructive tool proposed by [SPCdW05] for orbital stabilization of under-actuated nonlinear systems will be employed. The section starts by defining an Euler-Lagrange system, and listing the conditions a chosen virtual constraint must satisfy. Afterwards, the VC-based control methodology is proposed in section.III.3.a, and applied on the KGS in section.III.3.b.

Euler-Lagrange System

They are mechanical systems whose dynamics can be expressed by the Euler-Lagrange differential equation (eq.III.19). It can be also rewritten, as in [CM10], in the form:

D(q)¨q + C(q, q˙) + ▽P (q) = B(q)u (III.24)

Where: 74 III. Kite Generator System: Supervision

D(q) is the inertia matrix. • C(q, q˙) is the coriolis matrix. • ▽P (q) is the potential energy Matrix. • The system eq.III.24 is under-actuated if its control inputs are less than its degree of free- dom (DOF).

Feasible Virtual Constraints

The choice of the virtual constraint is determined by the system’s desired orbit; thus, its functionality. The virtual constraint should be regular and stabilizable [CM10]. In order to be regular, it should satisfy one of the three conditions of [CM10]-proposition 3.2. One of those is: B⊥.D(φˆ(θ)).φˆ′(θ) = 0 (III.25) 6 with φˆ(θ) = [θ φ(θ)] It is necessary as well that the virtual constraint is stabilizable; which means that, there exists a smooth feedback u(θ, θ˙) to enforce it. According to [CM10] parametric VCs are stabilizable.

Existence of Periodic Solution

As shown earlier, applying the VCs yields the reduced system of eq.III.21. Assume that:

There exists an equilibrium θ of the system in eq.III.21. • 0 α(θ), β(θ), γ(θ) are continuous on a vicinity O(θ ). • 0 There exists a continuous derivative of γ(θ) at θ = θ . • α(θ) 0

θ O, θ˙ with θ˙ < δ, δ > 0, the solution of the nonlinear system III.21 that • ∀ 0 ∈ 0 | 0| originates in this point is well-defined and unique.

According to [SRPS06]-Theorem 3, if an auxiliary linear system:

d2z d γ(θ) + .z = 0 (III.26) dt2 dθ α(θ)  θ=θ0 has a center at z = 0, then the nonlinear system III.21 also has a center at the equilibrium θ0. Furthermore, if the reduced system has at least one periodic solution then the same feed- back strategy, which is used to enforce the virtual constraints, results in generating a periodic motion for all the system’s degrees of freedom. III.3. Virtual Constraints-based Controller 75

III.3.a Methodology

The application of the VC-based control method can be summarized by the following steps:

Finding the Euler-Lagrange model of the system. • Choosing of a suitable virtual constraint. • Applying of a partial feedback linearization, where the remaining nonlinear part is • integrable.

Constructing of an auxiliary linear periodic control system of reduced order. • Designing of a LQR-based control for the auxiliary system. • Modifying of the control developed in the previous item to be applied to the original • nonlinear system.

These steps will be developed in detail in the following sections with a special attention to the studied KGS.

III.3.a-i KGS Under-actuated Model

For investigating the application of virtual constraints concept on the KGS, a simplified model of the later is considered. The chosen simplification matches the indoors tethered- wing prototype built and tested in GIPSA-Lab [HLAD13]. Here the KGS has two degrees of freedom, a translation along the tether r, and an angle θ. To have an under-actuated system, it is only controlled by one input that is the attack angle, α, while considering the tether tension constant. Fig.III.12 shows the reduced KGS and the GIPSA-Lab tethered- wing prototype.

Figure III.12: From the left: The indoors tethered-wing prototype of GIPSA-Lab and its representation.

The following notations are used hereafter: 76 III. Kite Generator System: Supervision

1 a = 2 ρaS 2 CL b = a( πλe + CD0 ) where ρa is the air density, A is the kite surface, λ is the kite’s aspect ratio, e is the Oswald efficiency factor, and CL,CD are the lift and drag coefficients as explained in Chapter.II. The effective wind velocity’s norm and angle, written in the polar coordinates r, θ, are expressed in eq.III.27.

2 ˙ 2 ˙ 2 We = (rθ cos θ +r ˙ sin θ) + (V + rθ sin θ +r ˙ cos θ) ˙ (III.27) α = arctan rθ cos θ+r ˙ sin θ w − V +rθ˙ sin θ+r ˙ cos θ   with V being the wind speed. Taking the previously defined notations, the KGS dynamic model is given in eqs.III.28 and III.29.

˙ ¨ 2r ˙θ 1 2 2 ∂CL θ + r + rM (bvr sin(θ αw) avr ( ∂α αw + CL0) cos(θ αw) + W cos θ) 2 − − − (III.28) avr ∂CL = cos(θ αw)αu ( rM ∂α − and

M ˙2 1 2 2 ∂CL r¨ M+M rθ + M+M (bvr cos(θ αw) + avr ( ∂α αw + CL0) sin(θ αw) W cos θ T ) − 2 IM IM − − − − avr ∂CL = sin(θ αw)αu ( M+MIM ∂α − (III.29) where M is the flying part mass and W is its weight, MIM is the rotor’s mass, αu the attack angle control, and T is the tension in the tether. As noticed, the dynamics can be reduced to a single equation with no input.

III.3.a-ii Reduced Dynamics system

As mentioned above, the objective of the VC approach is to find a reduced dynamics system by applying a partial feedback linearization. The KGS dynamics of eq.(III.28,III.29) can be equally expressed by eq.V.12.

θ¨ θ˙ D(θ, r) + C(θ, r, θ,˙ r˙) + ▽P (θ, r) = B(θ, r)αu (III.30) #r¨% #r˙% where:

The Inertia matrix is: • Mr 0 D(θ, r) = (III.31) # 0 (M + MIM ) %

The Coriolis matrix is: • 2Mr˙ 0 C(θ, r, θ,˙ r˙) = (III.32) Mrθ˙ 0 # − % The Potential energy function is: • bv2 sin(θ α ) av2( ∂Cl α + C ) cos(θ α ) W cos θ ▽ r w r ∂α w L0 w P (θ, r) = 2 − 2 ∂Cl − + bvr cos(θ αw) − avr ( αw + CL0) sin(θ αw) W sin θ + T − − ∂α −      (III.33) III.3. Virtual Constraints-based Controller 77

and the control matrix is: • ∂C cos(θ α ) B = av2 l − w (III.34) r ∂α sin(θ α ) # − w % Suppose that there exists a control law of the under-actuated system (eq.III.30) that makes the constraint presented in (eq.III.22) invariant then the overall closed-loop system results in an input-free reduced system of the form of eq.III.35. α(θ)θ¨ + β(θ)θ˙2 + γ(θ) = 0 (III.35) with

α(θ) = Mφ(θ) sin(θ αw) (M + MIM )φ′(θ) cos(θ αw) − − −

β(θ) = (Mφ(θ) (M + MIM )φ′′(θ)) cos(θ αw) − − +2Mφ′(θ) sin(θ αw) −

2 γ(θ) = bv W sin(αw) cos(θ αw)T r − − − where φ′(.) and φ′′(.) are respectively the first and second derivatives of the virtual con- straint with respect to θ. The chosen virtual constraint is stabilizable [CM10], because it is a parametric one. It must be regular as well, which implies that the system’s variables should respect the condition in eq.III.25; hence, satisfy the inequality: Mφ(θ)sin(θ α ) + (M + M )φ′(θ)cos(θ α ) = 0 − − w IM − w 6 Moreover, the resulted reduced system is a periodic Euler-Lagrange system [CM10] (Fig.III.13), which means that the same feedback strategy, used to enforce the VC, results in generating a periodic motion for all the system’s degrees of freedom [SRPS06].

Figure III.13: The reduced system periodic orbits.

The objective is to design the feedback controller that guarantees the invariance of the cho- sen virtual constraints and an orbital asymptotic stability of the chosen periodic solution. This control problem can be expressed in eq.III.36 y = r φ(θ) = 0, θ(t) = θ(t + T ) (III.36) − 78 III. Kite Generator System: Supervision

III.3.a-iii Partial feedback linearization

By introducing: r = y + φ(θ) r˙ =y ˙ + φ′(θ)θ˙ (III.37) r¨ =y ¨ + φ′′(θ)θ˙2 + φ′(θ)θ¨

The Euler-Lagrange system of eq.III.30, can be written in the coordinates (θ, y) as follows:

θ¨ θ˙ L(θ, y) + N(θ, y, θ,˙ y˙) = [B(θ, r)αu C(θ, r, θ,˙ r˙) ▽P (θ, r)] (III.38) y¨ − r˙ − r=y+φ(θ)    

1 0 0 with L(θ, y) = and N(θ, y, θ,˙ y˙) = . φ (θ) 1 φ (θ)θ˙2  ′   ′′  The dynamics of the variable y are given by:

y¨ = K(θ, y)u + R(θ, y, θ,˙ y˙) (III.39) where K(.),R(.) are given in eq.III.40.

2 ∂CL avr − ′ − − K(θ, y) = ∂α M(M+M )(y+φ) ( (M + MIM )φ cos(θ αw) + M(y + φ) sin(θ αw)) ′ IM ˙ φ ′ ˙ ˙ 2 − − 2 ∂CL − − ′′ ˙2 R(θ, y, θ, y˙) = M(y+φ) (2M(y ˙ + φ θ)θ + bvr sin(θ αw) avr ( ∂α αw + CL0)cos(θ αw) + W cosθ) φ θ 1 2 2 2 ∂CL + (M(y + φ)θ˙ + bvr cos(θ − αw) + avr ( αw + CL0)sin(θ − αw) − W cosθ − T ) M+MIM ∂α (III.40) According to eq.III.39, using the feedback transformation

1 u = K− (y, θ)[v R(θ, y, θ,˙ y˙)] (III.41) − results in a Partially linear system:

α(θ)θ¨ + β(θ)θ˙2 + γ(θ) = g (θ, θ,˙ θ¨)y + g (θ, θ˙)y ˙ + g (θ)v y y˙ v (III.42) y¨ = v  with

2 gy = (M sin(θ αw)θ¨ + M cos(θ αw)θ˙ ) − − − gy = 2M sin(θ αw)θ˙ ˙ − gv = (M + MIM ) cos(θ αw) −

As presented in [SFG10], if α(θ (t)) = 0, t [0,Tp], then the integration I defined in eq.III.43 ∗ 6 ∀ ∈ conserves a constant value on the reference orbit (θ , θ˙ ). ∗ ∗

˙2 θ∗ 2 θ∗ θ∗ θ 2β(τ) y0 2β(τ) 2γ(s) I(θ , θ˙ ) = ∗ exp( dτ) exp( dτ) ds (III.43) ∗ ∗ 2 − − α(τ) 2 − − α(τ) α(s) Zx0  Zx0 Zs )

Introducing the new coordinates ξ = [I, y, y˙]T , the system of eq.V.18 can be also represented by eq.III.44. 2θ˙ I˙ = [gy(t)y + gy(t)y ˙ + gv(t)v β(θ)I] α(θ) ˙ − (III.44) ( y¨ = v III.3. Virtual Constraints-based Controller 79

III.3.a-iv Controller Design The resulted incomplete nonlinear system of eq.III.44 plays an important role in developing a stabilizing controller. Its state-space representation is:

ξ˙ = A(t)ξ + b(t)v (III.45) with ξ = [I, y, y˙]T , and:

2θ˙ 2θ˙ 2θ˙ β(θ) gy(t) gy(t) − α(θ) α(θ) ˙ α(θ) A(t) =  0 0 1  0 0 0  T   2θ˙  b(t) = gv(t) α(θ) 0 1 h i One choice of the feedback controller v to exponentially stabilize the linear periodic system (eq.III.45) can be inspired from [SRPS05] where an LQR control is applied. The feedback controller can take the following form: 1 v = Γ− b(t)R(t)ξ (III.46) − T where R(t) is a symmetric matrix R(t) = R(t) for all t [0,Tp], periodic R(t) = R(t + Tp), and ∈ satisfies the Riccati equation:

T 1 T R˙ (t) + A(t) R(t) + R(t)A(t) + G = R(t)b(t)Γ− b(t) R(t)

Γ is a positive scalar and G is a (3 3) positive symmetric matrix. × The final obtained control diagram is shown in Fig.III.14. First, the KGS input is linearized through feedback. Then, the KGS model is reduced via insertion of the VCs. The introduction of the full integral I yields a partially linear system for which the stabilizer is designed.

Virtual Constraints

! Feedback !! Kite !!! !! !! !!! Coordinats !!! !!! !! transformation Model Change

!! Stabilizer

Reference orbit

Figure III.14: Control block diagram.

To end, the obtained solution for the reduced system of eq.III.35 is a solution of the closed-loop KGS system, which is expressed by Theorem.1.

Theorem 1. Given the under-actuated Euler-Lagrange KGS (eq.III.30) with 2 degrees of freedom (the tether’s inclination and length (θ, r)) and one control input (the attack angle α), and applying the virtual constraint results in the reduced system (eq.III.35) which has a time-periodic solution. Writing the dynamics of y and introducing the integral I (eq.III.43,III.39), results in the linear 80 III. Kite Generator System: Supervision

periodic in time system eq.III.45 completely controllable over the system’s period. Then the control solution eq.III.46 for the resulted system is exponentially orbitally stable solution for the closed-loop system (III.28), (III.29), (III.41), and (III.46).

The construction of the obtained solution implies that it is one of the solutions for the closed- loop system (Theorem 3 - [SPCdW05]).

III.3.b Application To show the effectiveness of the proposed feedback control, a simulation study was performed using the coefficients of the experimental set-up of GIPSA-Lab [HLAD13]. They are given in Ta- ble.III.3.b.

symbol name value M mass 0.1 Kg MIM rotor’s mass 0.0481 Kg ρ air density 1.225 Kg/m3 S wing area 0.1375 m2 e Oswald’s factor 0.7 λ aspect ratio 2.5 −1 ∂CL/∂α lift derivative w.r.t. α 0.05 deg CD0 zero lift drag 0.07 V mean air speed 6 m/s T The tether’s tension 3 N.m

Table III.3: Coefficients for the simulation study.

Our objective is to stabilize the system around a periodic orbit while controlling the attack angle only. Starting from an arbitrary point (θ, r, θ,˙ r˙) within the power region of the kite, the application of proposed virtual constraints-based control developed here gives the closed loop behavior of Fig.III.15. One can clearly see the effectiveness of the proposed feedback control. Several initial conditions have been tested and for all of them, the trajectories have stabilized on a periodic orbit in a short time. The speed of convergence depends on the gain of the feedback v control. In figure III.16, the evolution of ξ, which is the state of the partial linear system (III.45), is pre- sented. One can see the convergence of the integral I of equation (III.43). This means that system in closed loop is converging to the reference orbit. In Fig.III.17 and Fig.III.18, respectively, the temporal evolution of the tether’s length r and angle θ of the KGS and the applied controls are shown. Although these results may be improved through suitable choice of Γ and G, one can still see the effectiveness of the proposed control for this first approach. III.3. Virtual Constraints-based Controller 81

100

50

0 (°/sec)

d 50

100

150 75 80 85 90 95 100
(°)

Figure III.15: The closed loop system’s portrait.

2

I 0

2 0 5 10 15 20 25 30 0

0.1 y(m)

0.2 0 5 10 15 20 25 30 2

0 dy(m/sec)
2 0 5 10 15 20 25 30 t(sec)

Figure III.16: The partial linear system closed loop evolution. 82 III. Kite Generator System: Supervision

100

80 60 0 5 10 15 20 25 30 200

d 0
200 0 5 10 15 20 25 30 1

r 0.5 0 0 5 10 15 20 25 30 1

dr 0
1 0 5 10 15 20 25 30 t(sec)

Figure III.17: Evolution of state variables (θ, θ,˙ r, r˙) of the KGS.

Figure III.18: The applied control for the studied KGS. III.4. Conclusion 83

III.4 Conclusion

In this chapter, two methods to optimize and control the KGS were proposed and applied. The first strategy starts by defining a parametric orbit. The expression of the average generated power obtained following that orbit is written as a function of the radial velocity, and then maximized to find the optimal radial velocity and the orbit’s period. Once the orbit is found, a nonlinear model predictive control is applied to insure the orbit tracking by controlling the kite’s roll angle. The second strategy used a novel method in the field: Virtual constraints (VC). The method aims at reducing the system’s degrees of freedom by forcing virtual constraints between them. VC-based strategy was introduced and applied to a KGS moving in a pumping motion in 2D plane. The KGS has two degrees of freedom: A translation following the tether (r) and a rotation (inclination angle (θ)). It is controlled by the attack angle while the traction force determines the phase: Generation or recovery. By having one control input, the resulted system is an under-actuated Lagrangian system, and relations among the system’s variables (virtual constraints) are enforced by feedback to get an overall closed-loop periodic system that converges fast to the pre-planned motion. This first study on applying virtual constraints on a kite-based system has shown promising results that worth being explored more.

Chapter IV Kite Generator System: Grid Integration and Validation

Contents IV.1 Introduction ...... 87 IV.2 Power Transformation System ...... 87 IV.2.a Torque Transmission between the Kite and the PMSM ...... 88 IV.2.b The PMSM’s Vector Model ...... 88 IV.2.c Power Electronics Interface ...... 89 IV.3 Control Scheme ...... 90 IV.3.a Grid-connected operation ...... 91 IV.3.b Stand-alone Operation ...... 95 IV.4 KGS Control Validation ...... 96 IV.4.a Real-time Hybrid Simulation Systems ...... 97 IV.4.b Power Hardware In the Loop Simulator ...... 97 IV.4.c KGS Implementation on the PHIL Simulator ...... 98 IV.4.d Validation ...... 102 IV.5 Conclusion ...... 106

Abstract

The KGS is built to be grid integrated or to supply an isolated load. The mechanical power generated by the kite’s traction is translated into an electrical one via a perma- nent magnet synchronous machine (PMSM). This power is then injected in the grid or used to supply an isolated load after passing a power electronics interface that consists of two back to back three-phase voltage source converters: AC/DC and DC/AC. Two control schemes are developed for the both of operation modes: grid connected or stand-alone. The first case consists in active and reactive currents injection, while the second case consists in voltage/frequency control in order to supply a given isolated load. After assessing the proposed control strategy through simulations, experimental valida- tion is addressed. It is decidedly important to take into account the dynamic behavior of the system which cannot be well observed through mere simulations, as well as to monitor the impact of the neglected amounts in simulation. This is achieved via test- ing on a Power Hardware-In-the-Loop simulator which is a real-time hybrid simulation system.

IV.1. Introduction 87

IV.1 Introduction

In the ongoing research to decarbonize the electric grid as soon as possible without losing its reliability, grid integration of renewable energy resources is an important issue. Energy resources can be generating a DC power as in the case of a photovoltaic cell or an AC one as in wind turbines and hydroelectric generators. It may, as well, require a bi-directional grid interface or an energy storage as in relaxation-cycle systems. On the other hand, the resource may be used to supply a strong infinite grid, an isolated micro grid, or a given isolated load. Therefore, different topologies are proposed and developed depending on the nature of the energy resource and the usage. Both relaxation-cycle KGS and HPS, focused on in this thesis use a permanent magnet synchronous machine (PMSM) to translate the mechanic generated power to an electric one, then they require an AC/AC power electronics interface that insures a bi-directional power flow from/to the grid. In a stand-alone operation, this topology is reinforced by a storage unit because the system is not capable to supply the requested level of energy constantly, in addition to being a load itself during its recovery phase. The storage unit can be withdrawn by integrating more than one KGS or HPS to supply the same load. Herein, many solutions are proposed. In the case of an infinite grid connection mode, the system is required to harness the maximum possible power from the primary source (the wind or the waves in our application) and inject it into the grid. For this purpose a maximum power point tracking algorithm is necessary, except here, there is not a maximum power point but a maximum power cycle. In the case of a stand-alone operation, the goal is to achieve a certain level of power requested by the load, and the system’s cycle is chosen and controlled according to this demand. The proposed control strategies are tested through simulations and on a Power Hardware-In-the- Loop (PHIL) simulator. The current chapter is divided into three main parts. Firstly, section.IV.2 is dealing with the power transformation unit, ie. the PMSM and the power electronics interface. Secondly, section.IV.3 proposes the control scheme used to drive the power transformation unit for each connection mode: Infinite grid-connected and stand-alone operation. The third part of the chapter starts by introducing different real-time simulators briefly, then deals in more detail with the PHIL simulator in section.IV.4.b. In section.IV.4.c, the problem of implementing the KGS on the PHIL simulator is addressed and the experimental set up is presented. Finally, section.IV.4.d presents the simulations and the experimental results for the obtained models and control schemes.

IV.2 Power Transformation System

While a lot of research is being done to optimize the kite orientation control [NFM11][BO11] [AHB12], the grid connection part is yet to be treated. The kinetic power, captured from high altitude wind by the KGS, needs to be transformed into an electric one that can be injected in the electric grid or used to supply a certain load. For this purpose, a power transformation unit is needed. Among the proposed power transformation systems associated to renewable energy grid integration, the one shown in Fig.IV.1 offers a suitable solution for the relaxation-cycle nature of the studied systems. In the case of the KGS, the traction force of the kite is transformed into a torque applied on a permanent-magnets synchronous machine (PMSM) situated on the ground. This leads to producing 88 IV. Kite Generator System: Grid Integration and Validation

6$-& 19&"-,*%$"4:%-&,;!"&

7)!"#$%&' $(& 8).,$(' $(& 7) .,$(/
  )*%+&,-&, )*%+&,-&, 0*!(

1%&,2345-*,!2&

Figure IV.1: Kite Generator System Block diagram. an alternative electrical energy with variable frequency. The machine is coupled with the grid/load, through a power electronics interface that consists of two bidirectional AC/DC converters. An energy storage should be integrated in the case of a load or an isolated grid connection, in order to provide the necessary energy during the system’s recovery phase. It is installed on the DC-bus level relating the converters. The power transformation system is presented and modeled in the coming paragraphs.

IV.2.a Torque Transmission between the Kite and the PMSM The translation movement of the tether is transformed to a rotation by means of a drum coupled to the PMSM through a gearbox. Thus, the traction force Ftrac is translated to a torque CR applied on the machine. Torque transmission is expressed by the fundamental mechanical equation of eq.IV.1 and Fig.IV.2. dΩS CG CR DΩS = J (IV.1) − − dt where:

VL ΩS = is the rotation velocity, with K combining the gearbox factor and the drum diameter • K R. J is the total inertia of the kite, the drum; and the machine’s rotor. • CG is the generator torque. • D is the damping factor estimation. • and the transmission chain elasticity is neglected. Eq.IV.1 shows that in order to control the rotation velocity, a generator torque control should be applied, and vice-versa.

Figure IV.2: Modeling of the mechanic connection between the kite and the electrical machine.

IV.2.b The PMSM’s Vector Model Each machine’s phase can be presented by the Behn-Eschenburg equivalent electric model of Fig.IV.3, which consists of a resistance Rs, inductance Ls and an electromagnetic force esk : k = a, b, c. The model supposes the existence of a regular air gap, linear characteristics of the IV.2. Power Transformation System 89

Figure IV.3: PMSM’s Behn-Eschenburg equivalent electrical model. magnetic circuit (no saturation), and a balanced sinusoidal three-phase current behavior. To visualize the three phases at the same time, variables’ vector presentation is used, and is ex- pressed in Park frame (p, q) by

disd vsd = Rsisd + Ls dt ωLsisq disq − vsq = Rsisq + Ls dt + ωLsisd + ωφfsd φsd = Lsisd + φfsd (IV.2) φsq = Lsisq CG = pφfsdisq where

v¯s = vsd + j.vsq is stator voltages’ vector. • i¯s = isd + j.isq is stator currents’ vector. • φ¯fs = φfsd + j.φfsq is the induced flow vector. • p is the number of poles’ pairs. • ω = pΩs is the electric pulsation. • IV.2.c Power Electronics Interface The power electronics interface ensures frequency and voltage isolation between the PMSM and the electric grid or the connected loads, and at the same time it offers the possibility of power flow from/to the PMSM. This interface is made up of two converters AC/DC & DC/AC (Fig.IV.4,Fig.IV.5) [MBB10] that convert the variable frequency/voltage electric power generated by the PMSM, into a standard frequency/voltage electric power that agrees with the grid codes. A filtering stage precede the the connection and depends on its type. In Fig.IV.5, a filter L is used to connect the system to an infinite electric grid. The converters are controlled using vector pulse width modulation (PWM). Both converters func- tion as a rectifier and an inverter depending on the system’s phase (Generation or recovery), insuring a bi-directional transfer of energy. For the machine-side converter, supposing that the switches and voltage sources are perfect and the passive elements are linear and constant, Park representation of the converter’s average model is written in eq.IV.3:

disd UDC Ls dt = βsd 2 + ωLqisq Rsisd disq UDC − Ls dt = βsq 2 ωLdisd Rsisq esq (IV.3) dUDC − isd − isq − CDC = IDC + (βsd + βsq ) dt − 2 2 where UDC and IDC are the DC bus voltage and current respectively. 90 IV. Kite Generator System: Grid Integration and Validation

Figure IV.4: Electric representation of the PMSM-side converter. PMSM is presented by Behn- Eschenburg model. Cdc is DC-bus filtering capacitor.

Figure IV.5: Electric representation of the Grid-side converter. Rf and Lf represent loss and filtering components.

The same modeling approach is applied for the grid-side converter (Fig.IV.5):

diGd UDC √ Lf dt = βGd 2 + ωGLf iGq Rf iGd + 3VG diGq − UDC − Lf dt = βGq 2 + ωGLf iGd Rf iGq (IV.4) dUDC − iGd − iGq CDC = IDC (βGd + βGq ) dt REC − 2 2 where:

ωG is the electric grid pulsation of vres. • VG is the grid RMS voltage. • i¯G = iGd + iGq is the grid currents’ vector. • IDC is the machine converter output current. • REC As noticed, an average model is adapted in order to have a continuous time model without switching, which allows the usage of relatively large sampling time in simulations.

IV.3 Control Scheme

The control scheme is designed to insure: IV.3. Control Scheme 91

the tether radial velocity control to generate the desired average power taking into account • wind speed variations, and the electronics power interface electrical variables control. •

Figure IV.6: General control scheme of the KGS power transformation system. Two control tracks applied depending whether the system is grid connected or in a stand-alone operation.

Fig.IV.6 shows the general control scheme of the power transformation system. The control scheme is divided into three levels: Low, intermediate and high. Each level functions in accordance with the system operation status: Grid-connected or stand-alone operation. Both are presented and discussed in the following paragraphs.

IV.3.a Grid-connected operation When the KGS is connected to an infinite electric grid, the control strategy aims at harnessing the maximum available energy and injects it in the grid. Meanwhile the grid is responsible of supplying the necessary energy during the system’s recovery phase. For this purpose the machine-side converter is driven to control the machine rotation velocity, and the grid-side converter controls the DC-bus voltage and maintains the injected currents in phase with the grid voltages in order to preserve grid reliability.

IV.3.a-i Low Level Control The low level control concerns the converters switches control. It translates higher level control laws into pulse width modulation PWM commutation rates that command the converter’s switches. This conversion is done via control of the converters’ output currents or voltages according to the converter operation. In the case of infinite grid connection, both are current controlled.

The machine-side converter controls the generator torque CG via its current. Considering a PMSM and taking into account that the machine and its converter are working within their nominal limits; controlling CG is equivalent to controlling the current isq with asserting isd = 0 92 IV. Kite Generator System: Grid Integration and Validation

(See eq.IV.2). This allows having a maximum torque per ampere (MTPA). To control the currents, a PI controller acting in the p q rotating frame is used. It is simple yet − efficient for this control problem [BBM13][MBBR10]. The transfer function of such a controller takes the form: Ki 1 Hc(p) = Kp + = Kp(1 + ) (IV.5) p Tip with Ti = Kp/Ki, where: Kp, Ki are, respectively, the corrector proportional and integral gains. These parameters are chosen to let the current loop response time much faster than that of higher control loops, as well as, a limited overshoot that does not exceed the converters maximum currents. Fig.IV.7 shows the proposed control scheme in this case based on the converter’s model given by eq.IV.3, and with: E = pΩΦfsd. The control is done numerically in the p q space and a vector − PWM is built and transmitted to the a b c space to drive the switch. − −

茅 件鎚槌 紅鎚槌 戟帖寵 沈 鶏荊 に 件鎚槌

な " 詣鎚喧 髪 迎鎚 継

Figure IV.7: Low level control scheme for the machine-side converter.

茅 茅 The grid-side converter’s currents弔 must be in phase鎚槌 系憲堅堅結券建 with the grid voltages and have a low 茅 智 系 弔 件 鎚槌 harmonicよ distortion (THD). They鶏荊 are controlledな【計 in the fixed"系剣券建堅剣健" coordinates a 件b c via a resonant − − PI controller that acts on the current harmonies desired to詣剣剣喧 be eliminated [dHAEO06]. よ Such a controller take the following form: 継" 計帳 h 2K p H (p) = K + i (IV.6) c p p2 + ω2 n=1 n X弔 な 系 計弔 where the proportional gain Kp which" affects all the current harmonies equally, and the integral 蛍喧髪経 part Ki affects the h harmonies specified by their resonant pulse ωn. 眺 From Fig.IV.5, the grid-side converter current control系 scheme is shown in Fig.IV.8.

茅 IV.3.a-ii Intermediate茅 Level件弔銚 Control 紅弔銚 件弔椎 迎結嫌剣券欠券建""鶏荊 紅弔鳥 弔銚 The intermediate level control loops茅 generate件 the reference signals needed for the currents control 弔長 弔長 in the lower level via control穴圏 of件 the PMSM rotation velocity and紅 the DC欠決潔-bus voltage. 茅 迎結嫌剣券欠券建""鶏荊 弔槌 弔槌 【欠決潔 弔長 【穴圏 件 茅 紅 The rotation velocity is controlled by the件 Machine-side Converter弔頂 using a classic PI controller 件弔頂 紅 of the same form as that of eq.IV.5. It generates,迎結嫌剣券欠券建""鶏荊 according to the mechanical equation (eq.IV.1), the generator torque reference, hence isq件∗弔頂. 戟帖寵 Considering the current inner loop is much faster than that of the velocity, the resulted transfer に function is a second degree one from which the parameters of the PI corrector are determined. This is done by choosing a suitable time response that is much smaller than懸弔頂 the KGS cycle period, and な a suitable overshoot. Fig.IV.9 shows the rotation velocity" control loop, where KE = KG = pΦfsd 詣捗喧 髪 迎捗 懸頂 % 5ON @ON /CB L -) $ 5ON

#

,O9 P .O (

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&F ! ! ! % ! ! % 5EG ! @EG 5EM ! .4<8707= -) ! @EJ EG ! % 5 ! ! ! ! 3: 5EH ! @EH 012 % ! ! .4<8707= -) EN EN !012 EH ! !3: @ 5 % 5 EI EI 5 % ! @ 5ON .4<8707=@ON /-)CB L 5EI -) $ ! /CB ON 5 $ !

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&F Figure IV.9: Intermediate level control scheme for the machine-side converter: Machine velocity control. % % EG EG 5 @ EJ The grid-side converter5EM converts the direct power.4<8707= to a fixed-frequency -) alternative@ power, or vice EG versa, according to the KGS phase (Traction/Recovery),% 5 hence, it is driven to control the DC-bus 3: 5EH @EH 012 % voltage. .4<8707= -) EN EN !012 EH !3: 5 % @ 5 EI The DC-bus is assumed to have a resistance5EI R and a capacitor@C , and once again a vector DC .4<8707= -) DC PI controller is used to generate the i . Fig.IV.10 shows the DC-bus voltage resulted loop. Gq∗ 5EI /CB $ ! ! ! ! ! B ! EI B ab ? ab ]¥ K DSQQJNR! K ( ! ^dc # GE K K DONRQOL I , 9 P . FOOP ? (]¥ ! ! ! `_ A E Vab

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#%" ZkRl $71-49)9154 IV.3.a-iii High Level Control "5497522-7 #-+0)4183 YkXl In addition to generating the needed reference signals of the lowerkW=Y=W controlj= YjlkRl levels, the high level control supervises the functioning of the system by controlling the switches that determine the $..214- #%"' #)+014- i 81,- power flow through it. B $69131<)9154 TkXl !2/571903 U kRl "54:-79-7 "549752 WkXl

%)7)3-971+ $7*19 &;89-3 %)7)3-9-78 I=C=M=Q[= ? > 94 IV. Kite Generator System: Grid Integration and Validation

As observed in lower control layers, the PMSM’s rotational velocity control and the generator torque control are guaranteed by the PMSM-side converter. The kite applies a resistive torque CR that gives, when inserted in the mechanical equation, the rotation velocity ΩS. The velocity is corrected using a PI controller that yields a reference generator torque CGref . The reference rotation velocity is obtained by applying a maximum power “cycle” tracking (MPCT) algorithm that seeks the kite trajectory that guarantees a maximum average generated power.

IV.3.a-iv Maximum Power Cycle Tracking In the KGS, the optimal trajectory of the kite is a function of the wind speed and direction. In a certain direction, the optimal radial velocity changes its amplitude and period depending on the wind speed. Fig.IV.11 exhibits this dependence.

Figure IV.11: Optimal radial velocity as a function to time and wind speed.

In fact, the optimization algorithm proposed in sec.III.2.a-ii starts from a parametric orbit and finds the profile of the optimized normalized radial velocity, that isv ˆ(t), whose period Tn is also normalized. This result depends on the direction of wind only and the radial velocity profile is next found by:

VˆL =v ˆ V (IV.7) ∗ T = Tn/V (IV.8) with V being the wind speed. The proposed algorithm is a simple “Disturb & Observe” algorithm, whose objective is to find the multiplier V that should be applied on the normalized radial velocity profilev ˆ(t) to find the optimal radial velocityVˆL(t). In the case of absence of wind speed measurement, the optimal radial velocity can be calculated according to standard wind-altitude curves, while the MPCT algorithm acts on the rotation velocity amplitude and period to find the optimal profile. The algorithm begins by applying one period of the optimal radial corresponding to wind speed estimation. Then it calculates the average power during this period, and compares it later with the average power obtained after changing the multiplier V during the next period. Choosing to maximize the power on the whole cycle aims at ignoring fast short changes in wind speed The algorithm is effective to deal with slow changes in wind speed compared to the orbit’s IV.3. Control Scheme 95

period, which is usually valid for high altitude winds. Finally, the KGS complete proposed control scheme can be summarized in Fig.IV.12.

Figure IV.12: Inserting the MPCT algorithm in the NMPC-based proposed control strategy.

IV.3.b Stand-alone Operation

In a stand-alone operation, the KGS cannot insure a continuous deliverance of power to the con- nected load or isolated grid without the support of a storage unit or other energy resources. The second option can be achieved by supplying the load by more than one KGS whose orbits are suitably chosen in order to smooth the output power. For instance, Fig.IV.13 shows the output power profile resulting from using 4 kites flying in T/4 delay one from another and with a rotation 90◦.

Figure IV.13: Average output power of a 4-kite-based system.

Different kite generator systems are connected on the DC-bus level and share the same DC/AC inverter to connect the load or the micro grid. In fact, this is equivalent to considering a single KGS supported by a storage unit presented by other KGSs. The control levels vary slightly since the goal becomes generating the needed power for the load. The load-connected converter’s output voltages are controlled to have a constant amplitude and frequency. As a result, the machine-side converter(s) is (are) driven to control the DC-bus voltage, while the grid-side converter controls the AC output voltage. On the low control level, the machine-side converter is driven by currents as in the grid-connected operation case. Meanwhile, the load-side converter is controlled by voltages. 繋件券穴"劇┸ 建"

血件券穴"鶏岫酵岻┸ 茎岫酵岻"

96 IV. Kite Generator System: Grid Integration and Validation Œ̇®張岫邸岻 鶏岫酵岻" 系欠健潔憲健欠建結"懸岫建岻"

By adding an LC filter on the load-connected inverter, the converter and the load can be presented by the transfer function: 系欠健潔憲健欠建結"血岫建岻" 1 G(p) = (IV.9) p2 + ( 1 + Rf )p + 1 (1 + Rf ) RCf Lf Lf Cf R where the load is supposed to be resistive only R and Rf ,Lf ,Cf are the filter components.

茅 懸挑銚 紅挑銚 迎結嫌剣券欠券建""鶏荊 挑銚 茅 懸 懸挑長 紅挑長 迎結嫌剣券欠券建""鶏荊 挑長 茅 懸 懸挑頂 紅挑頂 迎結嫌剣券欠券建""鶏荊 懸挑頂 戟帖寵 に

な 態 捗 捗 " な 迎 な 迎 弔頂 喧 髪 磐 髪 捗 卑 喧 髪 磐な 髪 卑 懸 迎系 詣 詣系 迎 Figure IV.14: Load-connected converter low level control scheme.

In the intermediate control level, as in the case of grid connection, the machine-side converter controls the machine velocity, but via the DC-bus voltage control layer. The control scheme, shown in Fig.IV.15, results from eq.IV.2 and uses a PI corrector to regulate the DC-bus.

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&98 Figure IV.15: Machine-connected converter Intermediate level control scheme.

The high level control determines the sinusoidal 50Hz-frequency voltage reference for the load voltage loop and the DC-bus reference voltage.

IV.4 KGS Control Validation

The KGS model and control strategies will be tested through non-real time simulations. A following step will be to validate those experimentally. This is done usually via prototyping. Nevertheless, another direction is taken here, that is Power Hard-Ware-In-the-Loop (PHIL) simulation. For this purpose, an experimental bench built in G2Elab is put to service. It is a real-time hybrid simulator that consists the following main parts: IV.4. KGS Control Validation 97

A direct current machine (DCM). • A permanent magnets synchronous machine (PMSM). • A power electronics interface consisting of two converters (DC/AC, AC/DC) connected to a • grid emulator.

A real-time digital simulators: RT-lab and dSPACE that support and drive the previous • parts. In this simulator, the tethered kite behavior and its associated drum and gearbox are emulated by a direct current machine (DCM), while the rest of the system is physically present. The hardware is interfaced with the real-time simulator on which the optimization and the control strategy in addition to the kite model are implemented. Employing the PHIL-simulator instead of building a prototype is justified because the tests carried on here focuses on the grid integration aspect, and produced power maximization via control of the power conversion chain, and not on the kite orientation control. Furthermore, PHIL simulator has many advantages over the usage of a complete hardware prototype, it requires less material and human investments, it can be modified easily to test different control strategies, and allows experimenting different test conditions in the laboratory environment.

IV.4.a Real-time Hybrid Simulation Systems

A simulator is described to be real-time if its subsystems are able to communicate with each other efficiently. Real-time simulators are classified in three main groups: Analog, digital and hybrid. An analog simulator is composed of physically reproduced models or a reduction of the simulated system’s components. A real-time digital simulator is similar to a non-real-time one, except for its calculation step, which is fixed and sufficiently long to allow the systems components to perform required operations or calculations within it. The real-time analog simulator can be described as a reduced prototype, and it is specially useful to predict the dynamic behavior of the system and to test its regulators and sensors. On the other hand, it is costly and complex to reconfigured. These negative points are completely overcome in a real-time digital simulator, but still an analog simulator is superior when simulating complex-model components with high cut-off frequencies. A compromise or a combination of both is the hybrid real-time simulator. Such a simulator consists of two parts, a hardware containing the complex components of the system, usually the power ones, and a software part containing other components models and the control algorithms. Both parts are communicating with each other efficiently, meaning the software of the system is running on a fixed time step bigger the response time of the hardware. An example of the hybrid simulator is the hardware-in-the-loop presented in the next section and used later to validate the KGS.

IV.4.b Power Hardware In the Loop Simulator

The PHIL simulator is a semi-hardware semi-software system, in which measurements and control signals are exchanged between the hardware and the software. This technique of testing allows studying and validating energy management strategies while preserving the flexibility to modify the control and the test conditions. It is widely employed in aviation and automobile industries due to its important advantages: The possibility to simulate as many energy management strategies and architectures of con- • trol as desired with minimal intervention. 98 IV. Kite Generator System: Grid Integration and Validation

Reduced cost compared to the tests on actual system. • Facility and safety of application. • Nondestructive test. • A PHIL simulator was built in G2Elab. It was conceived during a few PhDs’ and masters’ projects [GEOBR06][MBAB10][ABR08]. Originally built to test the control strategies of wind and water turbines [BBM13][OGBR08][MBBR10][MBBG07][ABR08], it was later implemented to test Photovoltaics [CFBM10][GRBB11], electric vehicle traction chain [FTBV11][FBMB12], and others [AMCR14]. The hardware or physical part of the invested HIL-based simulator, presented in Fig.IV.16, is composed of a direct current machine (DCM) controlled to emulate the behavior of the primary energy source or load; and a PMSM coupled mechanically to the DCM and connected through two transistor-based converters with either an emulated infinite electric grid, or with a load. The software part contains the controllers and the model of the energy source.

Figure IV.16: PHIL Simulator

IV.4.c KGS Implementation on the PHIL Simulator

Simulation of the KGS using a software simulator is an important step to initially verify the per- formance of the proposed control strategy. An intermediate step before testing on a real prototype, is the test on the PHIL simulator. The simulator allows replication of the dynamic behavior of the real system with the possibility of controlling the working conditions in the laboratory [MBAB10] [And09]. The KGS power transformation unit is physically presented in the PHIL-simulator while the DC- machine replicate the behavior of the tethered kite.

IV.4.c-i KGS Scaling The real-time PHIL experimental bench in G2ELAB was not built for a single test set-up. Therefor, in order to employ the bench to test the dynamics of the KGS, a scaling stage is needed. The bench is characterized by:

Maximum power Pbmax = 3kW • IV.4. KGS Control Validation 99

Maximum rotation velocity Ωbmax = 314rad/s • Maximum torque Cbmax = 20Nm • The KGS parameters need to be chosen to adapt to these values, and a scaling factor is needed to be applied before inserting those in the experimental bench. Scaling the rotation velocity and the torque is expressed by: Cbmax = nCmax Ωmax (IV.10) Ωbmax = m Accordingly, the power scaling equation: n n P = C Ω = C Ω = P (IV.11) bmax bmax bmax m max max m max Notice that n = m necessarily since the objective of the proposed real-time simulation is to test 6 the dynamic behavior of the system and insure the functioning of the control strategy. However, the scaling factors are chosen to be the same in order to observe the delivered power losses.

IV.4.c-ii KGS Torque Emulation The experimental bench direct current machine is controlled to follow the dynamics of the KGS. As seen in section.IV.2.a, the mechanic connection between the tethered kite and the PMSM is expressed by the equation: dΩs CG CR DΩs = J (IV.12) − − dt with CR being the kite torque and Ωs the machine rotation velocity. Replacing the kite by the DCM results in the mechanic equation eq.IV.13

dΩE CG CDCM DEΩE = JE (IV.13) − − dt where:

CDCM is the DCM torque. • DE is the damping factor estimation between the DCM and the PMSM and it is a function • of the rotation velocity ΩE.

JE is the total inertia of the DCM and the PMSM. • Fig.IV.17 represents the mechanic connection for both mentioned cases. Comparing eq.IV.12 and eq.IV.13 yields that: in order to replicate the KGS behavior by the DCM, the ΩE’s dynamics have to follow that of Ωs and the DCM torque needs to be controlled to follow the reference in eq.IV.14. The resulted mechanic connection is represented in Fig.IV.18

dΩs C∗ = CR + (J JE) + (DE D)Ωs (IV.14) DCM − dt − Hence, the DCM torque reference consists of two parts, the tethered kite traction torque and a correction torque: dΩs Ccor = (J JE) + (DE D)Ωs − dt − However, computing Ccor is an issue in real-time applications since the rotation velocity gradient calculation induces noise, and determining the damping friction values is very difficult since they are functions of the rotation velocity [MBAB10]. In order to overcome these negative points, in [MBAB10] the authors modify the mentioned method by using the correction component Ccor to control the DCM rotation velocity to track that of the KGS drum. Applying that to the KGS results in the control block diagram presented in Fig.IV.19. 100 IV. Kite Generator System: Grid Integration and Validation

帳 帳 帳 よ鎚┸蛍┸経 よ ┸蛍 ┸ 経

Drum PMSM DCM PMSM 眺 弔 帖寵暢 帳 弔帳 帳 よ鎚┸蛍┸経% % % よ %┸蛍 ┸ 経

Figure IV.17: Representation%眺 %弔 of the Mechanic connection in the%帖寵暢 case of the%弔 KGS and the DCM.

よ聴┸系眺 Kite Model

茅 %帖寵暢 よ帳┸蛍帳┸ 経帳 聴 眺 よDCM┸系 Control

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DCM PMSM %帖寵暢 %弔 Figure IV.18: KGS replication using the DCM.

Notice that, once velocity tracking is insured, Ccor becomes constant which leaves the dynamics of CR only. A PI controller is used to insure tracking of the KGS rotation velocity [mun]. The controller has the general form: K H = K + I PI P p

The open-loop transfer function of the DCM rotation velocity according to the reference velocity is expressed as follows: Ω (p) J (K p + K ) E = E P I ΩS(p) (JEp + DE)p

Thus, the resulting closed-loop function is given in eq.IV.15.

τPI p + 1 Hcl = p2 2ξ (IV.15) 2 + p + 1 ωn ωn IV.4. KGS Control Validation 101

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$+*.-+))(- Figure IV.19: KGS replication using the DCM.

Where: KP τPI = KI ωn = √KI

1 DE ξ = + KP 2√KI JE   The corrector parameters are calculated according to the desired response, e.g. response time and overshoot, determined by ξ, ωn. The weak point of this corrector is that its parameters are dependent of the friction coefficient DE which is a function of the rotation velocity.

IV.4.c-iii Experimental Set-up

As mentioned earlier, the PHIL simulator is a hybrid semi-hardware semi-software one, in which the hardware part contains the electrical machines and the converters, while the software in- cludes the control of those as well as tethered kite model. The KGS test bench control scheme is shown in Fig.IV.21. The KGS parameters, the KGS orbit optimization (section.III.2.a-ii), the kite model (section.II.2.b) as well as the MPCT algorithm (section.IV.3.a-iv) are implemented on Matlab/Simulink. The simulink model has two outputs: The traction torque and the rotation velocity reference; and two inputs: The measured velocity and power. The simulink model communicate with RT-lab via a TCP/IP protocol functioning under Labview environment who play the role of a server for both. Here, the digital real-time simulator RT-lab provide a transparent interface with dSPACE. Using Labview to communicate data between Matlab/Simulink and RT-lab, avoids the necessity to modify the structures of already built and tested functionality on Simulink1.

!

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H ,)1 (?F>4EAC H # &JIK 102 IV. Kite Generator System: Grid Integration and Validation

On dSPACE, the torque emulator controller (section.IV.4.c-ii) generates the DCM torque refer- ence and send it to the digital signal processor DSPTMS320F 240 card that controls the DCM chopper. Meanwhile the control of the PMSM and the power electronics interface is performed on dSPACE. Fig.IV.21 shows an abstract scheme of the test bench control. Measurements of the rotation velocity, the generator torque and the DCM torque feed back the controllers.

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IV.4.d Validation

In this section the proposed control schemes are tested via simulation and on a PHIL simulator. The KGS’s parameters shown in Table.IV.1 are chosen in order to generate a radial velocity and traction torque that respect the limits imposed by the PHIL simulator [MBAB10]. The testing orbit is defined by the parametric equations (eq.IV.16) with a rotation 90o and τ [0, 2π]. ∈ θ(τ) = 55o + 10osin(2τ), φ(τ) = 15osin(τ) (IV.16)

Note that the orbit initial inclination is 55o which does not agree with the condition that let the assumption ‘The tether is straight and inelastic” true (See Sec.II.2.b). But, with a tether’s crosswind area much smaller than the kite surface, according to II.12, the tether’s drag force can be neglected in front of the kite traction force, so the previous assumption applies here. Applying the optimization algorithm proposed in section.III.2.a-ii results in the optimal tether radial velocity shown in Fig.IV.22 with a period T = 20.6sec. An optimal control that minimizes the cost function of eq.III.18 is applied to find the roll angle needed for the kite to track the optimal orbit. The resulted trajectory is shown on Fig.IV.23.

trac The tether’s optimized radial velocity VL as well as the traction force F obtained from the kite model are transformed into a rotation velocity ΩS and a torque CR applied to the rotor (see Fig.IV.2). The transformation is done through a drum coupled to the PMSM through a gearbox. IV.4. KGS Control Validation 103

Table IV.1: Kite Generator System Parameters

K 414 Gearbox factor * rotor diameter R (m) V 4 Wind speed (m/sec)

Ωmax 210 Maximum rotation velocity (rd/sec) Γmax 30 Motor maximum torque (N.m) p 4 Pole’s pairs number A, m 5, 3 Kite’s area(m2) and mass(Kg) 3 ρa 1.2 Air density (kg/m ) CL 1.2 Lift coefficient CD 0.08 Drag coefficient r0 600 Initial tether length (m)

Figure IV.22: Optimal normalized radial velocity.

The simplest representation of this transformation is a multiplication by a constant as in the following equations: F trac Ω = V K,C = (IV.17) S L R K In this case, the product factor K is found to be 414 in order to adapt to the PHIL simulator’s PMSM. The obtained velocity and torque are then applied on the Matlab/Simulink model of the power transformation system . The MPCT algorithm acts, as explained in section IV.3.a-iv, on the amplitude of the optimal radial velocity to follow slow changes of wind speed. To test the functioning of the MPCT algorithm, the wind speed is changed from 4m/sec to 5m/sec. Fig.IV.24 shows the modification of the velocity amplitude because of the MPCT algorithm, and the resulted resistive torque; and finally the development of the average power per period. The maximum power cycle (MPC) is seemed to be tracked in 3 times the orbit period which is about 60sec. The simulation shows that the estimated average produced power of the system, described in Table.IV.1, at a wind speed 5m/sec is 400W . The next step is to transform the mechanical power produced by the PMSM into an electrical power that can be injected into the grid. This can be insured by tuning different control levels paremeters presented in the general control scheme (Fig.IV.6). Remember that classical PID regulators are used to control the velocity and the currents of the machine-side converter, while for the grid-side converter’s currents a resonant PID is implemented.

Figs.IV.25 shows the machine phase current IaS and the DC bus UDC voltage during one period of the rotation velocity ΩS. It can be noticed that UDC is well controlled with an error less than 0.9%. Fig.IV.26 shows a grid phase current Ia G and the grid phases voltages Va,b,c G. The grid-side − − converter was successfully controlled to provide the grid with the current having only the 50Hz harmonic and is in phase with the voltage. 104 IV. Kite Generator System: Grid Integration and Validation

Figure IV.23: Orbit Tracking using optimal predictive control. In green: Traction phase, in red: Recovery phase.

Figure IV.24: Application of MPCT algorithm on the rotation velocity when wind speed changes from 4 to 5m/s at instant 40sec. Upper plot: In dashed red, the optimization resulted rotation velocity, in continuous blue, the MPPT rotation velocity. Center plot: The resistive torque (CR), in dashed red, at wind speed 4m/sec, in continuous blue, at 5m/sec. Lower plot: The average mechanic power.

The previous simulation results are a first and initial step towards the PHIL validation. We remind that in this test the control strategy is divided into two“independent”problems, the kite orientation, that is control of θ, φ through the roll angle ψ, and the radial velocity controlr ˙ through driving of the PMSM. Hence the MPPT algorithm acts only on ther ˙ regardless of the kite coordinates (θ, φ).

The setup of Fig.IV.21 was implemented to test the proposed control strategy. At a first step, radial velocity control via the PMSM, the torque emulation and the electrical variables control were tested through application of the optimized radial velocity VL and the kite torque CR resulted from KGS simulations in Chapter.III-section.III.2.b. VL and CR are scaled to match the experimental bench characteristics. As observed in Fig.IV.27, the resulting rotation velocity have cyclic profile that varies in the range [ 1000, 1000]RPM. Its variations are accompanied by synchronized equivalent variations in the − IV.4. KGS Control Validation 105



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Figure IV.26: Starting from upper figure: Grid voltages, grid current (IaG), its frequency analysis. kite torque, which shows how generated power is optimized from the machine point of view. These variations are translated by machine currents whose frequency, amplitude and phase change accordingly. The frequency is related directly to the rotation speed:

ω pΩ f = = 2π 2π

Meanwhile the current amplitude represents the torque variations, and the phase represents the rotation velocity direction changes. Notice as well that the DC-bus voltage keeps a constant value despite the variations in the rotation velocity. For the grid-side converter electrical variables, Fig.IV.28 shows the variations of the output current and the grid voltage following those of the rotation velocity. The current becomes zero before the rotation velocity reaches zero that is due to the losses in the converters elements. This explains also why the current amplitude is higher when the velocity is negative (Recovery phase) than when it is positive (Generation phase). Fig.IV.29 displays a closer look at current the voltage variations. It shows how the current is in π phase with the voltage during the generation phase, and 2 shifted during the recovery phase. 106 IV. Kite Generator System: Grid Integration and Validation

Figure IV.27: Starting from the upper plot: DCM torque (CDCM ), PMSM rotation velocity (Ωs), PMSM phase current (Isa), and DC bus voltage (UDC ).

IV.5 Conclusion

This chapter proposed and tested a solution to grid-integrate the KGS or use it to supply an isolated load. The solution is a power transformation unit consisting of a PMSM and a power electronics interface. For each connection type, a control scheme is proposed to insure the control of both the me- chanical and electrical variables of the power transformation chain. The control laws are tested via simulation then validated on a half-software-half-hardware experimental bench called a Power Hardware-In-the-Loop Simulator. Moreover, a Maximum Power Cycle Tracking algorithm was proposed to follow the optimal velocity profile that characterizes our relaxation cycle KGS in the case of slow variations of wind speed. This algorithm was tested on a Matlab/Simulink model of the system. Finally, a fast benchmarking setup based on the previous PHIL simulator was built and tested and is ready to be implemented for the purpose of testing the MPCT algorithms and to assemble the kite model and orientation part with the power transformation unit part. Further work will include testing under disturbances acting on the kite and will consider the case of unbalanced regimes. They will also take into account voltage dips propagating from the grid and the system’s LVRT (Low Voltage Ride Through) capabilities. The system can also achieve ancillary services via reactive power control for example. IV.5. Conclusion 107

Figure IV.28: Starting from the upper plot: PMSM rotation velocity (Ωs), grid phase current (Isa), and grid phase voltage (VGa).

Figure IV.29: Zoom into the grid voltage and current changes when the PMSM changes its rotation direction.

General Conclusions

Although a lot of development has been achieved recently in the renewable energy field, more needs to be done in order to avoid future problems accompanying oil depletion and dependence, as well as nuclear energy safety and public acceptance issues. Of those renewable energy resources, high altitude wind energy (HAWE) is a promising resource because of its availability and regularity. A solution to harness HAWE is the use of tethered kites. These simple structures allow us to reach high altitudes and transfer the wind energy mechanically to the ground where it is transformed into electrical and conditioned to integrate the grid. However, the limitations on tethers length and kite’s height require us to pull down the kite periodically which results in a system that periodi- cally generates/consumes energy and needs to be optimized to minimize the consumed power and maximizes the generation. The outcome system can be classified in the relaxation-cycles category. This thesis had as main objective the optimization and control of renewable energy systems with relaxation cycles and their grid integration. A secondary yet important objective was to provide a mapping on the latest trends in wind and wave energy domain. The work was conducted in Greno- ble electrical engineering laboratory G2Elab, with collaboration with the automatic department in GIPSA-Lab. A special attention was paid to a kite-based wind system, named “kite generator system”, as a representative of relaxation-cycle systems. It was chosen due to its simple structure yet complex dynamics and promising primary test results. The system is a part of the research on-going in GIPSA-lab on HAWE. After a brief presentation of energy history and expectations, different solutions to harvest wind energy at high altitude and offshore wave energy were over-viewed and compared. Two types were particularly addressed: The kite generator system and the heaving point-absorber system. They both result in a relaxation-cycle when controlled to generate a maximum average power. Those were our case study. As a first step, the simplified structure of each system as well as their power generation techniques were introduced and their models were developed. We noticed the similarity between both from the resulting power profile point of view. Hence, their grid integration problem can be handled similarly. However, since the kite-based system offers a set of very interesting problems when it comes to its flying part’s orbit choice and orientation, it was the one chosen to develop the control strategies on. The chosen KGS is a closed eight-shaped orbit: The generation (= traction) and the consumption (= recovery) phases occur during the same eight-shaped orbit. Two strategies to choose and control the orbit were proposed. 110 General Conclusions

Nonlinear predictive control (NMPC) based strategy: • Using a mathematical model of the system results in the expression of the average power as a function of the normalized tether’s radial velocity. Maximizing this power yields the kite’s orbit and radial velocity. A nonlinear model predictive control is applied to insure the orbit tracking by controlling the kite’s roll angle and the traction force. Virtual constraints control (VCC) based strategy: • That is a novel method used recently in Robotics. The KGS is controlled by the attack angle only while the traction force is fixed and determined by the phase: Traction or recovery; which means that the system is under-actuated, and is controlled by forcing some virtual constraints among its variables. To grid integrate the system or use it to supply an isolated load, a power transformation unit com- posed of a permanent magnet synchronous machine and a power electronics interface is proposed. In addition to insuring electrical variables control and accordance with the grid, the unit employs a Maximum Power Cycle tracking algorithm to follow the wind’s slow variations regardless of the wind speed measurements. It acts on the tether’s radial velocity. Models of this unit were found and control schemes in both connection cases were proposed and validated via simulations and on a real-time hybrid Power Hardware-In-the-Loop simulator. Another contribution of this thesis is a fast benchmarking setup based on the previous PHIL sim- ulator. This setup offers an interface built on RT-lab between the PHIL simulator and a real-time digital simulator without the need to adapt the algorithms and models codes to RT-lab require- ments, which facilitates and accelerates the testing procedure. It was built and tested and is ready to be implemented for the purpose of testing the MPCT algorithms and assembling the kite model and orientation part with the power transformation unit part. The work realized during the thesis opened doors to many other problems including both the en- ergy resource control and optimization and its grid integration. Next work will validate the KGS on the proposed fast benchmarking setup before testing on a prototype. It will also test the effect of the disturbances that may act on the kite, or results from the grid such as voltage dips and Low Voltage Ride Through. We propose as well adding a flywheel storage unit and test the system in a stand-alone scenario. Further work is to complete building an all automated prototype and to implement a more complex model of the KGS for flight simulation. Chapter V R´esum´eFran¸cais

V.1 Introduction

Pour r´epondre `ala demande ´energ´etique croissante et pour faire face A˜ l’´epuisement du p´etrole, ainsi que les effets n´egatifs de l’avancement industriel et technologique de l’homme sur le climat, plusieurs solutions ont ´et´epropos´ees. L’un des principaux d´efis est de d´ecarboniser le r´eseau ´electrique en ´eliminant les g´en´erateurs d’´electricit´ecombustibles, et les rempla¸cant de pr´ef´erence par des ressources qui respectent la nature et l’environnement et qui sont publiquement accept´ees. C’est o`ules ressources ´energ´etiques renouvelables soul`event comme une solution prometteuse. Derni`erement, beaucoup de recherche scientifique portant sur l’´energie renouvelable et qui visent `ar´esoudre ses probl`emes tels que l’efficacit´eet l’int´egration du r´eseau, et d’explorer des nouvelles m´ethodes et structures pour les exploiter. L’axe de recherche ult´erieure a conduit `ala naissance de syst`emes d’´energie renouvelable `acycle de relaxation. Ceux-ci ont un cycle de puissance p´eriodique avec deux phases : Une phase de g´en´eration au cours de laquelle le syst`eme fonctionne dans sa “r´egion de • puissance”, ce que lui permet de produire de l’´electricit´e jusqu’`ace qu’il atteigne ses limits. Une phase de r´ecup´eration qui r´einitialise l’´etat du syst`eme afin que une nouvelle phase • de g´en´eration d´emarre. Le syst`eme consomme de l’´energie pendant cette phase. Une op´eration d’optimisation est donc n´ecessaire pour assurer la minimisation de l’´energie con- somm´ee et la maximisation de celle g´en´er´ee, tout en respectant les diff´erentes contraintes sur le syst`eme lui-mˆeme, la source d’´energie primaire, le r´eseau ou encore les charges. Cette th`ese porte sur l’´etude de ces syst`emes de g´en´eration d’´electricit´e`acycle de relaxation. Des exemples de tels syst`emes comprennent les syst`emes de traction `abase d’aile volant, les syst`emes houlomoteurs (utilisant l’´energie des vagues ou de la houle) et certains syst`emes thermiques `abase d’´energie renouvelable. Dans ce cadre, deux exemples ont ´et´econsid´er´es : Syst`eme g´en´erateur de cerf-volant (KGS : Kite Generator System). Il s’agit d’une • solution propos´ee pour extraire l’´energie du vent stable et forte en haute altitude. Son principe de fonctionnement est d’entraˆıner m´ecaniquement une g´en´eratrice ´electrique au sol en utilisant un ou plusieurs cerfs-volants captifs. Syst`eme flotteur oscillant (HPS : Heaving Point-absorber System). C’est un syst`eme • d’´energie houlomotrice flottant qui emploie les oscillations des vagues pour tourner une g´en´eratrice ´electrique et produire de l’´electricit´e. Fig.V.1 montre la structure simplifi´ee de ce syst`eme. Ces deux syst`emes ont ´et´epr´esent´es et mod´elis´es pendant la th`ese, mais seulement le premier sera pr´esent´een d´etails dans les sections suivantes. Ceci parce que nous estimons que le syst`eme de traction `abase de cerf-volant port des d´efis plus importants et a un avenir prometteur. En plus des probl`emes classiques des ressources ´energ´etiques renouvelables, celles avec un cycle de relaxation sont un domaine de d´efis ouverts tr`es int´eressant, tels que la recherche de solutions 112 V. R´esum´eFran¸cais

Point-absorber

Power Gearbox transformation + Control Power Unit Line Sea Bed

Figure V.1: The HPS simplified structure. aux probl`emes d’optimisation multi-dimensionnelles et le raccordement au r´eseau. Ces d´efis sont abord´es dans cette th`ese r´ealis´eau seine du laboratoire de G´enie Electrique de Grenoble (G2ELab) en collaboration avec le laboratoire de Grenoble Images Parole Signal Automatique (GIPSA-Lab). Ce r´esum´ede th`ese est organis´ee en quatre parties principales : Le premier chapitre est une bref pr´esentation de l’histoire de l’´energie renouvelable et son ´evolution en concentrant sur l’´energie ´eolienne et plus pr´ecis´ement l’´energie ´eolienne a´eroport´ee. Le deux- i`eme chapitre pr´esent le syst`eme de traction `abase de cerf-volant choisit pour cette ´etude et sa mod´elisation. Dans le troisi`eme chapitre, les deux m´ethodes utilis´ees pour contrˆoler l’orientation et la stabilit´edu cerf-volant sont pr´esent´ees et test´ees en simulation. Le quatri`eme chapitre implique le probl`eme d’int´egrer le syst`eme cerf-volant sur le r´eseau ´electrique. Les chemins de contrˆole des variables m´ecaniques et ´electriques sont pr´esent´es et valid´es par des simulations ainsi que des tests sur un simulateur temps real (Hardware-in-the-loop Simulator).

V.2 Histoire

Plusieurs milliers des ann´ees en arri`ere l’´energie renouvelable ´etait la source unique d’´energie. Elle a ´et´eutilis´epour entrainer les bateaux au longues de la Nile en Egypte il y a 10 si`ecles. Les restes d’´eoliennes verticales en Iran (Fig.V.2) et les norias en Syrie sont des exemples du d´eveloppement pr´ecoce dans les technologies d’´energie renouvelable. N´eanmoins, l’´energie renouvelable a ´et´edomin´epar l’arriv´ee des combustibles fossiles dans le XIXe et XXe si`ecle. Ces combustibles ´etaient la base de la revolution industrielle. L’industrie automobile et la g´en´eration d’´electricit´e´etaient particuli`erement d´ependants de cette source d’´energie. En cons´equence, le d´eveloppement dans le domaine d’´energie renouvelable a pris beaucoup de recul. Fig.V.3 montre la dominance des ´energies fossiles depuis l’ann´ee 1965. La crise de 1973 aussi bien que les effets n´egatifs de r´echauffement de la plan`ete ont attir´el’attention encore une fois vers les ressources renouvelables qui promettent une ´energie propre et durable. Ces ressources sont en concurrence avec l’´energie nucl´eaire qui offrent des prix comp´etitifs mais reste tr`es peu accept´es publiquement et non accessibles `atous. Mˆeme si l’´energie produite par des ressources renouvelable r´epond au moins de 2% de la demande V.2. Histoire 113

Figure V.2: Eolienne verticale `aNishtafun en Iran (600 AD).

57#444

56#444

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Figure V.3: Consommation mondiale d’´energie par type de ressource.

´energ´etique globale, sa puissance install´ee, `apart celle de l’´energie hydraulique, a multipli´epar 5 pendant les deux derni`eres d´ecennies. Fig.V.4 montre la tendance selon laquelle la capacit´einstall´ee de l’´energie ´eolienne, solaire et celle g´eothermique a augment´e entre 1995 et 2012.

V.2.a Energie Eolienne Parmi les ressources renouvelable, l’´energie ´eolienne a subit la croissance la plus forte. En effet, sa capacit´e`amultipli´epar 9 depuis l’ann´ee 1995, ce qu’en fait la ressource avec la croissance la plus rapide de tous les temps. Cette ´energie est classiquement exploit´ee par des ´eoliennes. Un exemple de ceux-ci est repr´esent´e sur la Fig.V.5. Une telle ´eolienne est compos´ee d’un rotor avec 3 pales connect´edirectement soit ou soit par une boite `avitesse avec une g´en´eratrice. L’´eolienne est connect´ee directement ou via une interface d’´electronique de puissance avec le r´eseau ´electrique. La g´en´eratrice, le rotor et leur contrˆole sont port´es dans une nacelle sur un mˆat. Cette technologie a subit un d´eveloppement et une recherche intense pendant les derni`eres trois d´ecennies. Cette recherche a pour but l’augmentation de l’efficacit´eet la puissance nominale de l’´eolienne. En observant le d´eveloppement de l’industrie des ´eoliennes, une tendance d’augmenter leur taille est clairement distingu´ee. L’objective de ceci est de : Augmenter la surface de la r´egion de travail (A) avec la quelle la puissance moyenne croˆıt • lin´eairement. 114 V. R´esum´eFran¸cais

250,0

200,0

150,0

100,0

Million tonnes oil equivalentMillion 50,0

- 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Year

Geo Biomass Solar Wind

Figure V.4: Capacit´einstall´ee mondiale.

Augmenter la hauteur du rotor pour atteindre des vitesses de vent (V ) plus importantes, • r´eguli`eres et constantes. La Fig.V.6 montre un exemple de l’´evolution de la vitesse du vent en fonction de l’altitude. N´eanmoins, l’augmentation de la taille des ´eoliennes est accompagn´ee par des difficult´es techniques comme par exemple : la transportation, la maintenance et la fabrication, ainsi que l’investissement initial qui devient tr`es important. En fait, doubler la hauteur de l’´eolien multiplie le coˆut initiale par cinq! Et pourtant, 30% de la partie ext´erieur des pales est responsable de produire plus que 60% de la puissance nominale de l’´eolienne. En effet, le reste des pales ainsi que le mˆatsont principalement existant pour soutenir les pointes des pales et transf´erer l’´energie produite au sol. Ceci dit, et si nous r´eussissons `acontrˆoler les pointes des pales `avoler et exploiter l’´energie cin´etique du vent et puis la transmettre au sol par un cˆable? Cette id´ee est derri`ere le concept des ´eoliennes a´eroport´ees ou les ´eoliennes `ahaute altitude.

V.2.b Energie Eolienne A´eroport´ee L’id´ee d’utiliser les cerf-volants ou les ailes volants pour exploiter l’´energie du vent en haute altitude HAWE (High Altitude Wind Energy) est apparue dans les ann´ees soixante-dix mais le premier `a calculer l’´energie qui peut ˆetre g´en´er´ee par cette mani`ere est M.Loyd qui a publi´eses r´esultats dans le journal d’´energie en 1980. L’id´ee principale dans ce papier est qu’un aile volant dans un champ de vent (V ) vole `aune vitesse GeV o`u Ge est l’efficacit´ea´erodynamique de l’aile. Ceci est utilis´epour g´en´erer de l’´electricit´epar deux fa¸cons : La g´en´eration d’´energie `abord : Dans ce cas, la grande vitesse de l’aile est employ´ee • pour entrainer des ´eoliennes install´ees au bord et l’´energie ´electrique produite est ensuite transf´er´ee au sol par un cˆable conducteur. Ceci est appel´eaussi le mode de train´ee (Drag mode). La Fig.V.7 montre deux exemples des syst`emes qui utilisent ce principe : La matrice des ´eoliennes embarqu´ees de Joby et le Makani M1 de GoogleX. La g´en´eration d’´energie au sol : Dans ce cas, la force a´erodynamique r´esultante est • utilis´ee pour tracter le cˆable et trainer une machine ´electrique au sol, ceci est le mode de V.2. Histoire 115

Figure V.5: Eolienne classique `atrois pales.









 7©Æ§ 7©Æ§ ≥∞••§ ≠≥•£













(•©ß®¥ ≠

Figure V.6: Vitesse de vent en fonction de l’altitude.

portance (Lift mode). Fig.V.8 montre deux exemples de ces syst`emes : Le premier est l’utilisation des cerf-volants par SkySails pour augmenter l’efficacit´e´energ´etique dans les bateaux 30%, et le deuxi`eme est un prototype de KitGen en Italie.

L’´energie produite par les deux modes, est donn´ee par eq.V.1. En plus de la vitesse du vent, elle est une fonction des coefficients de portance CL et de train´ee CD de l’aile, la surface A et la densit´e d’air ρ. 2 C 2 P = ρAC L V 3 (V.1) max 27 L C  D 

Afin de voir le potentiel de cette id´ee, nous consid´erons un syst`eme ´eolien a´eroport´eavec les param`etres suivants : V = 13m/s, CL = 1,CD = 0.07. Un tel syst`eme a une densit´esurfacique de 40kW/m2 ce qui est 150 fois plus que le maximum de 0.26kW/m2 qui peut ˆetre obtenu par un syst`eme photovoltaique. Un autre exemple pour comparer : En construisant un system ´eolien a´eroport´erigide bas´esur les ailes d’un avion Airbus-380 dont le surface est 845m2 et l’envergure est 80m, le syst`eme r´esultant avec ses cˆables et g´en´erateurs aura un poids totale de 40tons et une puissance nominale de 30MW . Cette ´energie peut-ˆetre produite 116 V. R´esum´eFran¸cais

Figure V.7: A gauche : Le prototype de Joby, `adroite : Le Makani M1 prototype.

Figure V.8: A gauche : Un cerf-volant de SkySails , `adroite : Un prototype de KiteGen. par quatre ´eoliennes Enercon E126 dont chacune a une puissance nominale de 7.5MW et un poids 3100tons. Cela montre la quantit´edes mat´erielles qui peut-ˆetre ´economis´een utilisant cette tech- nologie. La recherche `aexploiter l’´energie de vent en haute altitude a d´ej`aattir´ee l’attention des dizaines d’´equipes acad´emiques et industrielles dans le monde surtout depuis l’ann´ee 2005. Parmi les pi- onniers, les ´equipes de recherche `ala Polytechnique de Turin en Italie (le projet KitGen) et `a l’universit´ede Delft aux Pays-bas, aussi que l’entreprise SkySail en Allemagne et Makani-Power aux Etats-Unis. Depuis 2008, la soci´et´ede l’Energie Eolienne A´eroport´ee organise une conf´erence multi-disciplinaire annuelle (Airborne Wind Energy Conference AWEC) qui pr´esent les derni`eres tendances et d´eveloppements dans ce domaine, y compris le design, les mat´erielles utilis´es, les m´eth- odes de contrˆole etc, ainsi que les d´efis aux quelles il faut faire face pour conduire la technologie jusqu’`ala commercialisation.

V.3 Syst`eme G´en´eratrice de Cerf-volant

Dans la suite, le syst`eme adopt´epour cette ´etude est pr´esent´eet mod´elis´e. Avant de montrer le choix du syst`eme, nous faisons une comparaison rapide entre les deux modes de g´en´eration dans les syst`emes ´eoliens a´eroport´es. En g´en´eral la g´en´eration au sol utilise des cerf-volants flexibles tandis que la g´en´eration `abord utilise des cerf-volants rigides. La comparaison est r´esum´ee sur le graphique de Fig.V.9. La g´en´eration `abord en utilisant des cerf-volants rigides offre une densit´esurfacique plus importante grˆace `aleur efficacit´ea´erodynamique mais la partie volant du syst`eme est tr`es complexe et lourde par rapport `aun syst`eme de g´en´eration au sol. Il est n´ecessaire d’utiliser un syst`eme de navigation embarqu´een plus de turbines. Les cerf-volants flexibles sont beaucoup plus simples `apiloter et leur partie volante est l´eg`ere ce qui augmente la sˆuret´edu syst`eme. En plus d’avoir une densit´e massique de puissance plus importante. Pour les raisons cit´ees ci-dessus, un syst`eme de traction `abase de cerf-volant a ´et´echoisi pour ´etudier ses probl`emes de contrˆole et d’int´egration au r´eseau. Dans les sections suivantes, la structure de ce syst`eme est pr´esent´ee ainsi que sa mod´elisation. V.3. Syst`eme G´en´eratrice de Cerf-volant 117

Figure V.9: La g´en´eration d’´energie `abord (Mode de train´ee) vs la g´en´eration d’´energie au sol (Mode de portance).

V.3.a Structure

La structure simplifi´ee du syst`eme ´eolien a´eroport´eadopt´esur cette ´etude est repr´esent´edans La Fig.V.10. C’est un syst`eme de traction `abase de cerf-volant nomm´e Kite Generator System (KGS). Le syst`eme est compos´ed’un cerf-volant attach´epar un seul cˆable au sol. Le cerf-volant est orient´epar un m´ecanisme install´e`ason niveau. Le cˆable transmet la traction caus´ee par la portance appliqu´ee sur le cerf-volant au sol o`uil entraˆıne une machine ´electrique. La puissance g´en´er´ee est inject´ee dans le r´eseau apr`es un passage par une interface d’´electronique de puissance.

Figure V.10: Structure simplifi´ee de KGS.

La trajectoire du cerf-volant peut prendre plusieurs formes, la plus populaire est en forme d’un huit allong´ece qui maximise le vent de travers souffl´esur le cerf-volant. Il y a deux possibilit´es dans ce cas :

Mode de pompage : Le cerf-volant suit la trajectoire tout en augmentant son altitude et • lorsque il arrive `ason altitude maximale, ou son longueur de cˆable maximal, il est tir´e vers le bas. Cette op´eration consume de l’´energie et le r´esultat est un cycle de g´en´era- 118 V. R´esum´eFran¸cais

tion/consommation. Mode d’orbite ferm´ee : O`ule cerf-volant reste sur une seule trajectoire ferm´ee pendent les • quelles deux phases d’op´eration sont distingu´ees : Une phase de g´en´eration pendant la quelle le cerf-volant est en train de voler directement dans la direction du vent de travers et il tracte le cˆable, et une phase de consommation o`ule cerf-volant est tirA˜ c afin de fermer la

trajectoire. L’existence d’un cycle de g´en´eration/consommation n´ecessite d’une ´etape d’optimisation afin de maximiser la puissance moyenne produite en respectant les contraintes du syst`eme comme la longueur de cˆable, sa traction, les angles de vol, etc.

V.3.b Mod´elisation Alors que l’objective de ce travail est d’optimiser et contrˆoler le KGS et les int´egrer dans le r´eseau ´electrique, des hypoth`eses r´ealistes suivantes sont prises en compte : Un mod`ele d’un point de masse pour le cerf-volant et son cˆable. Un tel mod`ele est rugueux • car il ne tient pas compte de la flexibilit´eet des d´eformations du cerf-volant mais il est utile pour contrˆoler et estimer la puissance g´en´er´ee. Une efficacit´ea´erodynamique ´elev´ee. • Un cˆable in´elastique et droit. Cette hypoth`ese est correcte lorsque la longueur du cˆable est • moins que 1000m et son inclinaison est inf´erieure `a80o. Les dimensions du cˆable permettent de n´egliger sa force de portance et consid´erer sa train´ee • seulement. Le vent est uniforme avec une direction non-variable ce qui est en accord avec l’effet que le • cerf-volant vole en haut altitude. Des informations sur la position et la v´elocit´edu cerf-volant sont fournies par des capteurs • et des observateurs. Les dynamiques de cerf-volant sont d´ecrites par la deuxi`eme loi de Newton :

aer m~γ = F~grav + F~ + F~trac (V.2)

Avec m la masse de cerf-volant, et ~γ est l’acc´el´eration :

rθ¨ + 2r ˙θ˙ rφ˙2 sin θ cos θ − ~γ = r sin θφ¨ + 2φ˙(r ˙ sin θ + rθ˙ cos θ) (V.3)   r¨ r(θ˙2 + φ˙2 sin2 θ)  −  aer La force a´erodynamique F~ est li´ee directement au vent effective We, qui est la diff´erence entre la vitesse de vent et la v´elocit´edu cerf-volant. Les composants de portance et de traˆın´ee sont exprim´ees par les equations V.4. Fig.V.11 montre les forces appliqu´ees sur le cerf-volant.

~ aer 1 2 FD = 2 ρaACD We ~xw aer − 1 | |2 (V.4) F~ = ρaACL We ~zw L − 2 | | Le mod`ele peut ˆetre pr´esent´edans la forme g´en´erale :

x˙(t) = f(x(t), u(t),P (t)) (V.5) avec des contraintes sur l’´etat x(t) et le vecteur de contrˆole u(t),

xmin x(t) xmax, umin u(t) umax (V.6) ≤ ≤ ≤ ≤ V.4. Optimisation et Contrˆole 119

Figure V.11: Les forces du cerf-volant.

L’´etat contient des informations sur la position et la v´elocit´ede cerf-volant repr´esent´ees dans les co- ordonn´ees sph´eriques, tandis que le contrˆole peut ˆetre import´esur l’angle de roulis, l’angle d’attaque et/ou la traction de cˆable. Fig.V.12 pr´esente les angles de vol command´ees. P (t) contient les effets externes qui influencent le comportement du syst`eme, comme par exemple : les perturbations de vitesse du vent et les creux de tension du r´eseau.

Figure V.12: A gauche : l’angle de roulis, `adroite : l’angle d’attaque.

La puissance moyenne produite par le syst`eme est le produit de la force de traction Ftrac et la vitesse radiale de cˆable VL : 1 T P¯ = F M (t)V (t)dt (V.7) M T trac L Z0 L’objective d’optimisation est de maximiser cela en respectant les limites physiques du syst`eme.

V.4 Optimisation et Contrˆole

Le syst`eme KGS d´ecrit dans la sec.V.3 est un syst`eme non-lin´eaire, complexe, instable dans la boucle ouverte avec des contraintes sur l’´etat et le contrˆole. Pour cela des m´ethodes non-conventionnelles sont n´ecessaires pour garantir le contrˆole de cerf-volant afin de suivre une trajectoire sp´ecifique qui maximise la puissance moyenne g´en´er´ee. Dans la suite, deux strat´egies d’optimisation et de contrˆole sont explor´ees. La premi`ere utilise la commande pr´edictive (Model predictive control MPC) et la deuxi`eme utilise une commande bas´ee sur les contraintes virtuelles (Virtual Constraints Control VCC).

V.4.a Commande Pr´edictive La strat´egie est pr´esent´ee dans la Fig.V.13 et peut ˆetre divis´ee en trois ´etapes : Choix d’orbite • 120 V. R´esum´eFran¸cais

Figure V.13: Strat´egie de contrˆole utilisant la commande pr´edictive.

La premi`ere ´etape commence par d´efinir une orbite param´etrique en forme d’un huit. L’orbite est pr´esent´ee par les ´equations suivantes :

θ(τ) = θ + cos(Rot)∆θ sin(2τ) sin(Rot)∆φ sin(τ) 0 − (V.8) φ(τ) = φ0 + sin(Rot)∆θ sin(2τ) + cos(Rot)∆φ sin(τ)

Avec : r0 la longueur initiale de cˆable, ∆θ, ∆φ, θ0, φ0 et Rot d´efinissent les variations des param`etres θ et φ (Fig.V.14).

Figure V.14: Initial orbit parameters.

Le choix de ces param`etres est essentiel pour d´eterminer la puissance maximale qui peut ˆetre exploit´e. Par exemple, cette puissance croˆıt avec la rotation d’orbite : Le maximum est `a o une rotation de 90 , et elle a une valeur maximale `aune certaine inclination θ0 qui d´epend de la nature du sol. La Fig.V.15 montre ces deux fonctionnalit´es. Optimisation de l’orbite • Le probl`eme d’optimisation comprend maximiser la puissance moyenne g´en´er´ee par le sys- t`eme en gardant la condition d’orbite ferm´ee. Ceci est repr´esent´ee dans le mod`ele math´ema- tique simplifi´ed´ecrit par Argatov [ARS09] par la suite :

¯ 1 2 3 max PM (v) = max ρaACLGeV J0(v) (V.9) v(τ) v 2   "
Avec : 2π vh(τ) dτ = 0 0 w v Z k − Le r´esultat de cette optimisation est la vitesse radiale du cˆablev ˆ(τ) et le vecteur de temps correspondant t(τ). V.4. Optimisation et Contrˆole 121

Figure V.15: En haut : La puissance m´ecanique moyenne en fonction de l’angle d’inclination θ0, en bas : En fonction de la rotation d’orbite Rot.

Poursuite de l’orbite • Les variables de r´ef´erence `asuivre sont la vitesse radial VL et la position angulaire θ(t) et φ(t). A fin de suivre la r´ef´erence, la vitesse radial est contrˆol´ee par la machine ´electrique au sol et l’angle de roulis ψ est command´epour orienter le cerf-volant et suivre les angles θ(t) et φ(t). La commande pr´edictive cherche de commander l’angle ψ qui minimise la fonction de coˆut :

2 min (¨xref x¨) + λ1 (x ˙ ref x˙) + λ2 (xref x) u k − − − k

Avec x = [θ, φ, θ,˙ φ˙] et u = ψ. L’application Table.V.1 montre les param`etres principaux du syst`eme KGS, et Fig.V.16 montre les orbites de teste. Orbite 2 est le r´esultat de pivoter la premi`ere orbite `a 90◦, tandis que l’orbite 3 est le r´esultat de l’amplification de l’orbite 1.

Table V.1: Les param`etres du syst`eme cerf-volant KGS

V 4 Vitesse de vent (m/s) A 5 Surface du cerf-volant (m2)

CL 1.5 Coefficient de portance CD 0.15 Coefficient de tra ˆın´ee

Les profils des vitesses radiales optimales sont montr´es dans la Fig.V.17. Pivoter l’orbite `a90◦ s’est traduit par doubler la p´eriode de profil de vitesse, ainsi que doubler les dimensions d’orbite conduit aussi `adoubler la p´eriode de vitesse radiale. Table.V.2 inclut les valeurs de puissance moyenne et p´eriode correspondantes `achaque orbite. Ces r´esultats ´etaient attendus et sont en accord avec les r´esultats de [ARS09].

V.4.b Les Contraintes Virtuelles Les contraintes virtuelles sont des relations entre les variables d’un syst`eme Lagrange sous-actionn´es forc´ees par une feedback. Cette id´ee a ´et´ed´ej`a´etudi´ee et appliqu´ee dans le domaine de la robotique pour r´esoudre des probl`emes de balance et des mouvements p´eriodiques. Parmi les applications : 122 V. R´esum´eFran¸cais

Figure V.16: Orbite param´etriques de teste.

Figure V.17: La vitesse radial optimale correspondante.

Le Rabbit robot, le pendule invers´ee, etc. En g´en´eral, un syst`eme est exprim´edans eq.V.10 o`u:

q = [q , q , ..., qn] est le vecteur des coordonn´es g´en´eralis´es etq ˙ est son vecteur de v´elocit´e. • 1 2 u est le vecteur des entr´ees de commande et B est la matrice de contrˆole. • L(q, q˙) est le Lagrangian de syst`eme. • Ce syst`eme est sous-actionn´esi : dim(u) < dim(q) . d ∂L ∂L ( ) = B(q)u (V.10) dt ∂q˙ − ∂q

Renforcer des contraints virtuelles qui relient tous les coordonn´es [q2, ..., qn] `a q1 m`ene au syst`eme auxiliaire avec un cycle limite exprim´edans eq.V.11.

2 α(q1)q ¨1 + β(q1)q ˙1 + γ(q1) = 0 (V.11)

Selon [SPCdW05], la strat´egie de r´etraction utilis´ee pour renforcer les contraintes virtuelles m`ene `ala g´en´eration d’un mouvement p´eriodique de tout les d´egr´ees de libert´edu syst`eme. Cette id´ee est employ´ee pour assurer la suite et la stabilisation du syst`eme cerf-volant KGS sur une orbite. L’application des contraintes virtuelles pour contrˆoler le vol de cerf-volant est une nouvelle approche propos´ee pour la premi`ere fois avec cette th`ese. Dans cette application, un KGS qui fonctionne en V.4. Optimisation et Contrˆole 123

Table V.2: La p´eriode et la puissance moyenne des orbites optimis´ees

Orbite 1 2 3

PM (W ) 240 840 844 P´eriode (s) 35.4 35.0 78.4

mode pompage en deux dimensions est choisit. Ce mod`ele repr´esente le indoors prototype r´eduit construit et test´e`aGIPSA-Lab [AHB11a]. Le cerf-volant a deux d´egr´ees de libert´e: une translation r et une rotation θ et il est contrˆoler en commandant l’angle d’attaque α, ceci est repr´esent´edans Fig.V.18. La force de traction est constante dans ce cas.

Figure V.18: KGS en mode pompage en deux dimensions.

La m´ethodologie suivie est pr´esent´ee dans la Fig.V.19. Les ´etapes de celle-ci sont expliqu´ees par la suite.

Figure V.19: Diagramme de la m´ethodologie VCC.

Le Mod`ele Sous-actionn´ede KGS • Le mod`ele adopt´epour le syst`eme est donn´epar :

θ¨ θ˙ D(θ, r) + C(θ, r, θ,˙ r˙) + ▽P (θ, r) = B(θ, r)α (V.12) r¨ r˙ u     124 V. R´esum´eFran¸cais

o`u:

– La matrice d’inertie est :

Mr 0 D(θ, r) = (V.13) 0 (M + M )  IM  – La matrice de Coriolis est :

2Mr˙ 0 C(θ, r, θ,˙ r˙) = (V.14) Mrθ˙ 0  −  – La fonction d’´energie potentielle est :

bv2 sin(θ α ) av2( ∂Cl α + C ) cos(θ α ) W cos θ ▽ r w r ∂α w L0 w P (θ, r) = 2 − 2 ∂Cl − + bv cos(θ αw) − av ( αw + CL ) sin(θ αw) W sin θ + T  − r −   r ∂α 0 −    (V.15) – et la matrice de contrˆole est :

2 ∂Cl cos(θ αw) B = avr − (V.16) ∂α sin(θ αw)  −  Les Dynamiques R´eduites • En appliquant le contraint virtuelle : r = h(θ)

les dynamiques r´eduites r´esultantes de syst`eme sont :

α(θ)θ¨ + β(θ)θ˙2 + γ(θ) = 0 (V.17)

La Lin´earisation en feedback Partielle • Alors que l’objective de contrˆole est d’assurer que (y = r h(θ) = 0), le changement de − coordonn´ees de [r, θ, r,˙ θ˙] `a[y, θ, y,˙ θ˙] est plus repr´esentative du probl`eme. Le r´esultat de ce changement de coordonn´ees est un syst`eme partiellement lin´eaire

α(θ)θ¨ + β(θ)θ˙2 + γ(θ) = g (θ, θ,˙ θ¨)y + g (θ, θ˙)y ˙ + g (θ)v y y˙ v (V.18) y¨ = v 

En [SRPS05], les auteurs proposent d’ajouter une nouvelle variable I qui exprime la distance de l’orbite de r´ef´erence et qui facilite le design de stabilisateur. Les nouvelles coordonn´ees ξ = [I, y, y˙]T m`enent `ala repr´esentation de eq.V.19.

2θ˙ I˙ = [gy(t)y + gy(t)y ˙ + gv(t)v β(θ)I] α(θ) ˙ − (V.19) ( y¨ = v

Le Design de Contrˆoleur • La repr´esentation d’´etat du syst`eme lin´eaire variant dans le temps (eq.V.19) est :

ξ˙ = A(t)ξ + b(t)v (V.20)

Le choix de la variable de feedback v peut ˆetre inspir´ede [SRPS05] o`uun contrˆoleur LQR classique est utilis´e. V.4. Optimisation et Contrˆole 125

L’application Afin de montrer l’efficacit´ede cette m´ethode, une simulation sur Matlab qui utilise les param`etres de prototype indoors de GIPSA-Lab est r´ealis´ee. L’objective est de stabiliser le cerf-volant autour d’une orbite p´eriodique en contrˆolant l’angle d’attaque seulement. La Fig.V.20 montre l’orbite de r´ef´erence et l’orbite du cerf-volant dans l’espace de phase (θ, θ˙). La Fig.V.21 montre l’´evolution des variables du syst`eme ainsi que le contrˆole de l’angle d’attaque. Renforcer les contraintes virtuelles a donn´elieu `aun syst`eme exponentiellement stable sur son cycle limite, et le r´esultat est que tout les d´egr´es de libert´edu syst`eme finissent par suivre un mouvement pA˜ c riodique.

Figure V.20: Le phase plot.

Figure V.21: D´eveloppement des variables du syst`eme. 126 V. R´esum´eFran¸cais

V.5 Int´egration au R´eseaux

L’int´egration du syst`eme cerf-volant (KGS) sur le r´eseau ´electrique ou son utilisation pour alimenter une certaine charge est r´ealis´e`atravers d’une interface de transformation de puissance. Cette interface est repr´esent´ee sur la Fig.V.22.

Figure V.22: Evolution des variables du syst`eme.

L’interface est compos´ee d’une machine ´electrique qui transforme la puissance m´ecanique exploit´ee par le cerf-volant et transmise par le cˆable en puissance ´electrique avec une fr´equence variable. Celle-l`aest ensuite standardis´ee et inject´ee dans le r´eseau ou utilis´ee pour alimenter une charge. Dans la suite, l’interface de transformation de puissance est d´etaill´ee et mod´elis´ee puis son chemin de contrˆole est pr´esent´e. Ensuite, un simulateur Hardware-In-the-Loop (HIL) qui permet de tester les chemins de contrˆole propos´es est pr´esent´eainsi que l’impl´ementation de KGS sur celui-ci. En fin, les r´esultats de validation de KGS en simulation et sur le HIL sont pr´esent´es.

V.5.a L’Interface de Transformation de Puissance

La transmission de couple entre le cerf-volant et la machine ´electrique est exprim´ee par l’´equation m´ecanique (eq.V.21) dΩS CG CR DΩS = J (V.21) − − dt o´u:

VL ΩS = est la vitesse de rotation, avec K combine le facteur de la boˆıte de vitesse et le • K diam`etre du tambour R. J est l’inertie totale du cerf-volant, de tambour et de rotor. • CG est le couple g´en´erateur. • D est l’estimation de facteur d’amortissement. • La chaˆıne de transformation de puissance est repr´esent´ee dans la Fig.V.23. La machine utilis´ee est une machine synchrone `aaimants permanents pr´esent´ee par son mod`ele ´electrique de Behn- Eschenburg. Deux convertisseurs `atransistors sont impl´ement´es pour installer le KGS sur le r´eseau ou pour alimenter une charge isol´ee.

Figure V.23: Repr´esentation ´electrique de la machine synchrone `aaimants permanents et les convertis- seurs AC/DC et DC/AC. V.5. Int´egration au R´eseaux 127

Afin de contrˆoler le flux d’´energie dans la chaˆıne, le chemin de contrˆole de la Fig.V.24 est appliqu´e. Il est divis´een trois niveaux :

Figure V.24: Chemin de contrˆole g´en´erale de l’interface de transformation de puissance.

Niveau bas de contrˆole • Ce niveau g´en`ere les signaux MLI (Modulation de largeur d’impulsion) qui contrˆolent la fermeture et l’ouverture des interrupteurs des convertisseurs afin de contrˆoler, soit le courant, soit la tension des convertisseurs selon le type de connexion (R´eseau ou charge).

Niveau interm´ediaire de contrˆole • Ce niveau de contrˆole g´en`ere les r´ef´erences n´ecessaires pour le niveau pr´ec´edent. La vitesse de la machine est contrˆol´ee par le convertisseur cˆot´emachine. La tension de bus continu est contrˆol´ee soit en commandant le courant du convertisseur cˆot´er´eseau dans le cas de connexion r´eseau, soit en contrˆolant la vitesse de rotation de la machine en cas de connexion avec une charge.

Niveau haut de contrˆole • Ce dernier niveau de contrˆole est responsable de g´en´erer les signaux de r´ef´erence manquants et contrˆoler le flux d’´energie dans l’ensemble. Deux cas sont distingu´es :

– La connexion au r´eseau fort infini Dans ce cas, le KGS injecte la puissance g´en´er´ee dans le r´eseau pendant sa phase de g´en´eration et il obtient la puissance n´ecessaire pour sa phase de r´ecup´eration du r´eseau. Ici, le convertisseur cot´emachine contrˆole la vitesse de rotation de la MSAP afin de maximiser la puissance moyenne et le convertisseur cot´er´eseau contrˆole la tension du bus continu. – La connexion avec une charge isol´e Ce cas n´ecessite l’addition d’un stockage d’´energie pour alimenter le KGS pendent sa 128 V. R´esum´eFran¸cais

phase de r´ecup´eration. Le convertisseur cot´emachine contrˆole la tension du bus continu et celui cot´echarge contrˆole la tension qui aliment la charge.

Au plus, ce niveau de contrˆole inclut un algorithme de poursuite de maximum de puissance qui ressemble `aun algorithme de “Maximum power point tracking” utilis´edans les ´eoliennes classiques pour chercher la vitesse de rotation qui maximise la puissance. Dans le cas du syst`eme KGS, l’algorithme cherche le profile de vitesse radiale de cˆable qui maximise la puissance moyenne, dans ce cas l’algorithme est nomm´e: Maximum Power Cycle Tracking (MPCT).

V.5.b Validation Afin de valider les strat´egies de contrˆole propos´ees, un banc exp´erimental “Hardware-In-the-Loop” construit `aG2ELAB est utilis´e. Ce banc offre: Une flexibilit´epour tester des sc´enarios de gestion de l’´energie illimit´ee et des architectures • de contrˆole diff´erentes sans devoir changer la structure physique du plateforme; Un coˆut r´eduit par rapport `aun prototype; • Une facilit´eet s´ecurit´ed’application; • Un contrˆole non destructif. • Dans ce banc la partie volant de syst `eme KGS ainsi que le tambour sont remplac´es par une machine `acourant continue, bien que le reste du syst`eme (MSAP + interface d’´electronique de puissance) est physiquement existant. Le mod`ele de cerf-volant aussi bien que les lois de commande des variables m´ecaniques et ´electriques du syst`eme sont impl´ement´es sur un simulateur digital. Fig.V.25 repr´esente le HIL banc exp´erimental et Fig.V.26 montre les mesures des diff´erents variables du syst`eme en simulation et sur le HIL simulateur.

Figure V.25: Repr´esentation du banc exp´erimental.

V.6 Conclusion

Ceci est un r´esum´efran¸cais de th`ese intitul´e“Optimisation de contrˆole commande des syst`emes de g´en´eration d’´electricit´e`acycle de relaxation”. Le r´esum´e a commenc´epar un introduction du sujet de th`ese et focaliser sur la pr´esentation de case d’´etude qui est le syst`eme de traction `abase de cerf-volant (Kite Generator System : KGS). Ce syst`eme a ´et´emod´elis´eet deux m´ethodologies de contrˆole ´etaient pr´esent´ees afin d’optimiser son orbite et garantir la suivie ainsi que la stabilisation V.6. Conclusion 129

Figure V.26: Validation des chemins de contr ˆoles: A gauche en simulation, A droite sur le HIL simula- teur. de cerf-volant sur cette orbite. La premi`ere m´ethode utilise l’approche de commande pr´edictive (Model predictive control : MPC) qui a ´etait d´ej `autilis´edans la bibliographie et a montr´edes r´esultats tr`es satisfaisant, `apart le temps de calcul de contrˆole qui est important. La deuxi`eme m´ethode utilise une nouvelle approche celui de renforcement des contraintes virtuelles (Virtual constraints control : VCC). Cette approche est inspir´ee de la robotique o`uelle a ´et´eappliqu´ee dans des dizaines des application afin de r´esoudre les probl`emes de mouvement periodic et de stabilit´e. On a montr´ela possibilit´ed’appliquer le VCC sur le syst`eme KGS et des r´esultats prometteurs ont ´et´etrouv´e. En suite, le probl`eme d’int´egration du syst`eme cerf-volant sur le r´eseau, ce que n’a pas ´et´etrait´e auparavant, a ´et´eadress´e. L’interface avec le r´eseau a ´et´epr´esent´ee ainsi que les chemins de commande complets pour le cas de connection avec un r´eseau fort infini ou une charge isol´ee. Le test de ces chemin a ´et´eaccomplit par les simulation et sur un simulateur Hardware-in-the-loop. Ce travail est un premier au niveau de la France dans le domaine d’´energie de vent en haut altitude. C’est une base tr`es riche pour d´emarrer des travaux avenir dans: Le contr ˆole de la partie volant du syst `eme en prenant compte des variation de direction de • vent, les perturbation, le vol sans vent, etc. L’int´egration sur un r´eseau isol´eet prendre en compte l’effet de creux de tension, l’addition • d’un stockage qui utilise un flywheel, etc. G´en´eraliser les r´esultats obtenus sur des autre syst`emes `a cycle de relaxation. •

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International journals

Mariam Ahmed, Ahmad Hably, Seddik Bacha, Kite Generator System Modeling and Grid In- tegration, Sustainable Energy, IEEE transactions on, Vol 4, No 4, Octobre 2013, Pages 968-976.

International conferences

Mariam Ahmed, Ahmad Hably, Seddik Bacha, Kite Generator System Periodic Motion Planning Via Virtual Constraints, IECON 2013 - 39th Annual Conference of the IEEE Industrial Electronics Society, Austria-Vienna, Pages 1-6.

Mariam Ahmed, S-C Murillo-Cruz, Ahmad Hably, Seddik Bacha, A comparative study on a pump- ing wave energy conversion system, Industrial Electronics (ISIE), 2012 IEEE International Sym- posium on, China- Hangzhou, Pages 1419-1424.

Mariam Ahmed, Ahmad Hably, Seddik Bacha, High altitude wind power systems: A survey on flexible power kites, Electrical Machines (ICEM), 2012 XXth International Conference on, France- Marseilles, Pages 2085-2091.

Mariam Ahmed, Ahmad Hably, Seddik Bacha, Grid-connected kite generator system: Electrical variables control with MPPT, IECON 2011 - 37th Annual Conference on IEEE Industrial Electron- ics Society, Australia-Melbourne, Pages 3152-3157.

Mariam Ahmed, Ahmad Hably, Seddik Bacha, Power maximization of a closed-orbit kite gen- erator system, Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference on, USA-Orlando, Pages 7717-7722.